Isothermal reversible ideal gas system The concepts deals with system in which the temperature of the system is constant With the help of this animation user will be able to do expansion and contraction of the system at the constant temperature and check how does the isotherm is plotted By Rachit Agarwal Department of chemistry IIT Bombay

Instruction for user temperature T pressure P volume V start end Master layout Pressure tab Temperature tab volume tab Heat, change in enthalpy, work and change in internal energy displays graph Up and down arrow key Start and end button Instruction box pistonweight Systemthermometer HeatQ workW Change in enthalpy Change in Internal energy

1)A constant temperature will be maintained during the process. 1)User can choose a temperature from the list given (this list will be shown in the instruction box) 1)User can change either volume or the pressure and other parameter pressure or volume respectively will be changed by following the law PV= NRT (N=1) 1)The parameter can by changed by using the down and up arrow tabs 1)Both the pressure and volume have their limit pressure 1 to 50 atm, volume from 1 to 50 lts 1)Start button – used to start the process 1)End button – used to stop the process 1)The graph should be plotted simultaneously once the user click the start button till the user presses the end button, even for the change in 0.5 units the graph should be plotted Instructions for the animator: Working of the animation select the temperature from the following 150k 300k 450k 600k start end

Instructions for the animator: Plotting of the graph The x axis of the graph is the volume and the y axis of the graph is the pressure Scale X axis 1 cm = 10 Lts of volume Y axis 1cm = 10 atms of pressure Eg For P= 25 and V = 4 The red dot shows the mark For P = 2 and V = 50 The blue dot shows the mark And then both the line are joint by a curve line such that the P*V is constant i.e. for the above case P*V is 100 units, so the curve joining both the points should maintain the above relationship as shown in the graph by black curve

Definition and rules for the users An isothermal is a process in which the temperature is maintained constant during the process, the graph of P v/s V is called as the isotherm at the constant temperature The change in internal energy in isothermal process is zero (dU = nCvdT) work done is given by integral of –PdV, using the first law of thermodynamics the Q (heat) can be calculate as ∆u = Q + w, which implies the Q = -w as change in internal energy change for isothermal process is zero (dU = nCvdT) the enthalpy can be calculated as H = U + PV, U and PV both are constant, therefore the change in enthalpy is zero for isothermal process User will read the instruction in the instruction box and then follow the steps as said It will choose a temperature at which the system process has to be carried Then he will choose any of the two parameter i.e. pressure or volume and enter the initial value of one of the parameter, the value of the other parameter will come automatically by using the equation PV=nRT, here n =1, both pressure and volume have limits of 1 to 50 units each Then the user will click the start button and can change the selected parameter using the arrows tab and reach his final destination and then click the end button to stop the process and to get the values of work, heat, change in internal energy and change in enthalpy

Analogy / Scenario / Action / Example Volume gradient: the size of the yellow box signifies the volume 100mm = 50lts and The size equal to 2mm = 1lts e.g. Initially yellow box (60mm in height) signifies the volume which is equivalent to 50 units, the finally yellow box (30mm in height) signifies the volume which is equivalent to 25 units Pressure gradient: the color code (R:G:B 255:0:0) signifies the pressure equal to 1 atm and color code (R:G:B 0:0:0) signifies the pressure equal to 50 atm e.g. initially red bar (255:0:0) signifies the pressure = 1atm and finally the bar (127:0:0) signifies pressure = 2 atm 100mm 50mm Initial stage Final stage

Instruction for user Step 1 initial ActionDescriptionAudio narration enter temperatureAllow the user to click the temperature tab Please click the temperature tab Circle the temperature tabOnce the user clicks the temperature tab Make a yellow circle behind it click the temperature tab temperature T start end

Instruction for user Step 1 final ActionDescriptionAudio narration enter temperatureAllow the user to click the temperature tab Please click the temperature tab Circle the temperature tabOnce the user clicks the temperature tab Make a yellow circle behind it click the temperature tab temperature T start end

Instruction for user Step 2 initial ActionDescriptionAudio narration TemperatureAllow the user to select the temperature from the list Please select the temperature from the list in the instruction box Circle the temperature selectedOnce the user select the temperature Make a yellow circle behind it and enter that particular value in the box above the temperature tab e.g. 300 select the temperature from the following 150K 300K 450K 600K Instruction for user temperature T start end

Instruction for user Step 2 final ActionDescriptionAudio narration TemperatureAllow the user to select the temperature from the list Please select the temperature from the list in the instruction box Circle the temperature selectedOnce the user select the temperature Make a yellow circle behind it and enter that particular value in the box above the temperature tab e.g. 300 select the temperature from the following 150K 300K 450K 600K temperature T start end 300K

Instruction for user Step 3 initial ActionDescriptionAudio narration Select the parameterAllow the user to click either on pressure or the volume tab Please click the pressure or volume tab, the parameter you want to change Circle the parameter selectedOnce the user select the pressure or the volume tab Make a yellow circle behind it E.g. case 1 pressure Case 2 volume click on the one of the tab from pressure or volume that you want to change temperature T start end 300K pressurevolume

Instruction for user Step 3.1 final ActionDescriptionAudio narration Select the parameterAllow the user to click either on pressure or the volume tab Please click the pressure or volume tab, the parameter you want to change Circle the parameter selectedOnce the user select the pressure or the volume tab Make a yellow circle behind it E.g. case 1 pressure Case 2 volume click on the one of the tab from pressure or volume that you want to change temperature T start end 300K pressurevolume

Instruction for user Case 1 Step 4.1 (pressure) initial ActionzDescriptionAudio narration Using the up and down arrow key1 atm should be displayed as default in pressure tab Allow the user to click the up and down arrow key On click the up key increase pressure by 0.5 atm and on clicking the down arrow key decrease the pressure by 0.5 atm (do not across the range 1atm to 50 atm), the value should change in the box above the pressure tab Range is from 1 atm to 50 atm with 0.5 atm as least count Click startAllow the user to click the start button e.g the initial value set by the user is 5 atm set the initial pressure from where you want to start the process using the down and up arrow key, range 1 atm to 50 atm with 0.5 atm as least count then click the start tab to start the process temperature T pressure P volume V start end 300K

Instruction for user Case 1 Step 4.1 (pressure) final ActionzDescriptionAudio narration Using the up and down arrow key1 atm should be displayed as default in pressure tab Allow the user to click the up and down arrow key On click the up key increase pressure by 0.5 atm and on clicking the down arrow key decrease the pressure by 0.5 atm (do not across the range 1atm to 50 atm), the value should change in the box above the pressure tab Range is from 1 atm to 50 atm with 0.5 atm as least count Click startAllow the user to click the start button e.g the initial value set by the user is 5 atm set the initial pressure from where you want to start the process using the down and up arrow key, range 1 atm to 50 atm with 0.5 atm as least count then click the start tab to start the process end ` temperature T pressure P volume V 5 atm start 300K end

Instruction for user Case 1 Step 5.1 (pressure) initial ActionDescriptionAudio narration Enter the value of the volumeIn the box above the volume tab enter the value calculated as (T*.0821/P) lts, in this case it is The initial volume is (T*.0821/P) lts (speak the calculate vale) i.e lts Change the height of yellow box and colour of piston (bar) As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changes The gradient for the color and height is given by analogy slide The volume is calculated using the equation PV= NRT end temperature T pressure P volume V 5 atm start 300K end

Instruction for user Case 1 Step 5.1 (pressure) final ActionDescriptionAudio narration Enter the value of the volumeIn the box above the volume tab enter the value calculated as (T*.0821/P) lts, in this case it is The initial volume is (T*.0821/P) lts (speak the calculate vale) i.e lts Change the height of yellow box and colour of piston (bar) As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changes The gradient for the color and height is given by analogy slide The volume is calculated using the equation PV= NRT end temperature T pressure P volume V 5 atm start 300K lts end

Instruction for user Case 1 Step 6.1 (pressure) initial ActionDescriptionAudio narration Draw the graphPlot the initial point on the graph, in this case at p= 5 and v = by red dot Using the up and down arrow keyAllow the user to click the up and down arrow key On click the up key increase pressure by 0.5 atm and on clicking the down arrow key decrease the pressure by 0.5 atm (do not across the range 1atm to 50 atm), the value should change in the box above the pressure tab. Eg shown for 0.5 atm change Your process has started, please change the value of pressure to change the state of the system and then click the end button once the process is over Change the height of yellow box and colour of piston (bar) As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changes The gradient for the color and height is given by analogy slide Draw the graphSimultaneously draw the graph of P v/s V Eg shown for 0.5 atm change by blue dot Draw both the points with a black line Your process has started, please change the value of pressure to change the state of the system and then click the end button once the process is over end temperature T pressure P volume V 5 atm start 300K lts end

Instruction for user Case 1 Step 6.1 (pressure) final ActionDescriptionAudio narration Draw the graphPlot the initial point on the graph, in this case at p= 5 and v = red dot Using the up and down arrow keyAllow the user to click the up and down arrow key On click the up key increase pressure by 0.5 atm and on clicking the down arrow key decrease the pressure by 0.5 atm (do not across the range 1atm to 50 atm), the value should change in the box above the pressure tab. Eg shown for 0.5 atm change Your process has started, please change the value of pressure to change the state of the system and then click the end button once the process is over Change the height of yellow box and colour of piston (bar) As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changes The gradient for the color and height is given by analogy slide Draw the graphSimultaneously draw the graph of P v/s V Eg shown for 0.5 atm change by blue dot Draw both the points with a black line Your process has started, please change the value of pressure to change the state of the system and then click the end button once the process is over end temperature T pressure P volume V 5.5 atm start 300K lts end

Instruction for user Case 1 Step 7.1 (pressure) initial Action`DescriptionAudio narration Using the up and down arrow keyAllow the user to click the up and down arrow key On click the up key increase pressure by 0.5 atm and on clicking the down arrow key decrease the pressure by 0.5 atm (do not across the range 1atm to 50 atm), the value should change in the box above the pressure tab. Value of volumeThe value of the volume will change every time the pressure is changed By the formula (T*.0821/P) lts Change the height of yellow box and colour of piston (bar) As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changes The gradient for the color and height is given by analogy slide Draw the graphSimultaneously draw the graph of P v/s V eg the end value reached by the user is P=50 atm then the value is shown by green dot, and a black line is drawn joining all the blue points that came by increment in 0.5atm Your process has started, please change the value of pressure to change the state of the system then click the end button once the process is over end temperature T pressure P volume V 5.5 atm start 300K lts end

Instruction for user Case 1 Step 7.1 (pressure) final ActionDescriptionAudio narration Using the up and down arrow keyAllow the user to click the up and down arrow key On click the up key increase pressure by 0.5 atm and on clicking the down arrow key decrease the pressure by 0.5 atm (do not across the range 1atm to 50 atm), the value should change in the box above the pressure tab. Value of volumeThe value of the volume will change every time the pressure is changed By the formula (T*.0821/P) lts Change the height of yellow box and colour of piston (bar) As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changes The gradient for the color and height is given by analogy slide Draw the graphSimultaneously draw the graph of P v/s V eg the end value reached by the user is P= 50 atm then the value is shown by green dot, and a black line is drawn joining all the blue points that came by increment in 0.5atm Your process has started, please change the value of pressure to change the state of the system then click the end button once the process is over end temperature T pressure P volume V 50 atm start 300K lts end

Instruction for user Case 1 Step 8.1 (pressure) initial DescriptionAudio narration End buttonAllow the user to click the end button when ever he wants toYour process has started, please change the value of pressure to change the state of the system and then click the end button once the process is over Value in boxes from heat and work tab Enter the value in the enthalpy box as 0 J, internal energy as 0J and the value of work as (= *T*ln(Pi/Pf)) J, where Pi is the starting pressure and Pf is the final pressure. And heat as -W E.g. the final pressure by user is 25 atm then the work is = J, And heat is Change in internal energy and change in internal energy will be zero because the process is isothermal, the work is (= *T*ln(Pi/Pf)) and heat is -W Your process has started, please change the value of pressure to change the state of the system and then click the end button once the process is over end temperature T pressure P volume V 50 atm start 300K lts end

Instruction for user Case 1 Step 8.1 (pressure) final DescriptionAudio narration End buttonAllow the user to click the end button when ever he wants toYour process has started, please change the value of pressure to change the state of the system and then click the end button once the process is over Value in boxes from heat and work tab Enter the value in the enthalpy box as 0 J, internal energy as 0J and the value of work as (= *T*ln(Pi/Pf)) J, where Pi is the starting pressure and Pf is the final pressure. And heat as -W E.g. the final pressure by user is 50 atm then the work is = J, And heat is J Change in internal energy and change in internal energy will be zero because the process is isothermal, the work is (= *T*ln(Pi/Pf)) and heat is -W Your process has started, please change the value of pressure to change the state of the system and then click the end button once the process is over end temperature T pressure P volume V 50 atm start 300K lts end HeatQ workW Change in enthalpy Change in Internal energy 0 J J J

Instruction for user Step 3.2 final ActionDescriptionAudio narration Select the parameterAllow the user to click either on pressure or the volume tab Please click the pressure or volume tab, the parameter you want to change Circle the parameter selectedOnce the user select the pressure or the volume tab Make a yellow circle behind it E.g. case 1 pressure Case 2 volume click on the one of the tab from pressure or volume that you want to change temperature T start end 300K pressurevolume

Instruction for user Case 1 Step 4.2 (volume) initial ActionzDescriptionAudio narration Using the up and down arrow key1 lts should be displayed as default in volume tab Allow the user to click the up and down arrow key On click the up key increase volume by 0.5 lts and on clicking the down arrow key decrease the volume by 0.5 lts (do not across the range 1lts to 50 lts), the value should change in the box above the volume tab Range is from 1 lts to 50 lts with 0.5 lts as least count Click startAllow the user to click the start button e.g the initial value set by the user is 5 lts set the initial volume from where you want to start the process using the down and up arrow key, range 1 lts to 50 lts with 0.5 lts as least count then enter the start tab to start the process temperature T volume V pressure P start end 300K

end ` Instruction for user Case 1 Step 4.2 (volume) final ActionzDescriptionAudio narration Using the up and down arrow key1 lts should be displayed as default in volume tab Allow the user to click the up and down arrow key On click the up key increase volume by 0.5 lts and on clicking the down arrow key decrease the volume by 0.5 lts (do not across the range 1lts to 50 lts), the value should change in the box above the volume tab Range is from 1 lts to 50 lts with 0.5 lts as least count Click startAllow the user to click the start button e.g the initial value set by the user is 5 lts set the initial volume from where you want to start the process using the down and up arrow key, range 1 lts to 50 lts with 0.5 lts as least count then enter the start tab to start the process temperature T volume V pressure P 300K 5 lts start

Instruction for user Case 1 Step 5.2 (volume) initial ActionDescriptionAudio narration Enter the value of the pressureIn the box above the pressure tab enter the value calculated as (T*.0821/V) atm, in this case it is atm The initial pressure is (T*.0821/V) atm (speak the calculate vale) i.e atm Change the height of yellow box and colour of piston (bar) As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changes The gradient for the color and height is given by analogy slide The pressure is calculated using the equation PV= NRT end temperature T volume V pressure P 300K 5 lts start

Instruction for user Case 1 Step 5.2 (volume) final ActionDescriptionAudio narration Enter the value of the pressureIn the box above the pressure tab enter the value calculated as (T*.0821/V) atm, in this case it is atm The initial pressure is (T*.0821/V) atm (speak the calculate vale) i.e atm Change the height of yellow box and colour of piston (bar) As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changes The gradient for the color and height is given by analogy slide The pressure is calculated using the equation PV= NRT end temperature T volume V pressure P 300K 5 lts start atm

Instruction for user Case 1 Step 6.2 (volume) initial ActionDescriptionAudio narration Draw the graphPlot the initial point on the graph, in this case at v= 5 and p = by red dot Using the up and down arrow keyAllow the user to click the up and down arrow key On click the up key increase volume by 0.5 lts and on clicking the down arrow key decrease the volume by 0.5 lts (do not across the range 1lts to 50 lts), the value should change in the box above the pressure tab. Eg shown for 0.5 lts change Your process has started, please change the value of volume to change the state of the system and then click the end button once the process is over Change the height of yellow box and colour of piston (bar) As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changes The gradient for the color and height is given by analogy slide Draw the graphSimultaneously draw the graph of P v/s V Eg shown for 0.5 lts change by blue dot Draw both the points with a black line Your process has started, please change the value of volume to change the state of the system and then click the end button once the process is over end temperature T volume V pressure P 300K 5 lts start atm

Case 1 Step 6.2 (volume) final Instruction for user ActionDescriptionAudio narration Draw the graphPlot the initial point on the graph, in this case at v= 5 and p = by red dot Using the up and down arrow keyAllow the user to click the up and down arrow key On click the up key increase volume by 0.5 lts and on clicking the down arrow key decrease the volume by 0.5 lts (do not across the range 1lts to 50 lts), the value should change in the box above the pressure tab. Eg shown for 0.5 lts change Your process has started, please change the value of volume to change the state of the system and then click the end button once the process is over Change the height of yellow box and colour of piston (bar) As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changes The gradient for the color and height is given by analogy slide Draw the graphSimultaneously draw the graph of P v/s V Eg shown for 0.5 lts change by blue dot Draw both the points with a black line Your process has started, please change the value of volume to change the state of the system and then click the end button once the process is over end temperature T volume V pressure P 300K 5.5 lts start atm

Action`DescriptionAudio narration Using the up and down arrow keyAllow the user to click the up and down arrow key On click the up key increase volume by.5 lts and on clicking the down arrow key decrease the volume by 0.5 lts (do not across the range 1lts to 50 lts), the value should change in the box above the volume tab. Value of pressureThe value of the pressure will change every time the volume is changed By the formula (T*.0821/v) atm Change the height of yellow box and colour of piston (bar) As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changes The gradient for the color and height is given by analogy slide Draw the graphSimultaneously draw the graph of P v/s V eg the end value reached by the user is v= 50 lts then the value is shown by green dot, and a black line is drawn joining all the blue points that came by increment in 0.5atm Case 1 Step 7.2 (volume) initial Instruction for user Your process has started, please change the value of volume to change the state of the system and then click the end button once the process is over end temperature T volume V pressure P 300K 5.5 lts start atm

Case 1 Step 7.2 (volume) final end temperature T volume V pressure P 300K 50 lts start atm Action`DescriptionAudio narration Using the up and down arrow keyAllow the user to click the up and down arrow key On click the up key increase volume by.5 lts and on clicking the down arrow key decrease the volume by 0.5 lts (do not across the range 1lts to 50 lts), the value should change in the box above the volume tab. Value of pressureThe value of the pressure will change every time the volume is changed By the formula (T*.0821/v) atm Change the height of yellow box and colour of piston (bar) As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changes The gradient for the color and height is given by analogy slide Draw the graphSimultaneously draw the graph of P v/s V eg the end value reached by the user is v= 50 lts then the value is shown by green dot, and a black line is drawn joining all the blue points that came by increment in 0.5atm Instruction for user Your process has started, please change the value of volume to change the state of the system and then click the end button once the process is over

Case 1 Step 8.2 (volume) initial end temperature T volume V pressure P 300K 50 lts start atm Instruction for user Your process has started, please change the value of volume to change the state of the system and then click the end button once the process is over DescriptionAudio narration End buttonAllow the user to click the end button when ever he wants toYour process has started, please change the value of volume to change the state of the system you can also click on the pressure tab to change the pressure and then click the end button once the process is over Value in boxes from heat and work tab Enter the value in the enthalpy box as 0 J, internal energy as 0J and the value of work as (= *T*ln(Vf/Vi)) J, where Vi is the starting volume and Vf is the final volume. And heat as -W E.g. the final volume by user is 50 lts then the work is = J, And heat is

Case 1 Step 8.2 (volume) final end temperature T volume V pressure P 300K 50 lts start atm Instruction for user Your process has started, please change the value of volume to change the state of the system and then click the end button once the process is over DescriptionAudio narration End buttonAllow the user to click the end button when ever he wants toYour process has started, please change the value of volume to change the state of the system you can also click on the pressure tab to change the pressure and then click the end button once the process is over Value in boxes from heat and work tab Enter the value in the enthalpy box as 0 J, internal energy as 0J and the value of work as (= *T*ln(Vf/Vi)) J, where Vi is the starting volume and Vf is the final volume. And heat as -W E.g. the final volume by user is 50 lts then the work is = J, And heat is HeatQ workW Change in enthalpy Change in Internal energy 0 J J J

Links for further studies References books PETER ATKINS, JULIO DE PAULA – PHYSICAL CHEMISTRY 8 TH EDITION SIVA PLS ADD SOME BOOKS

Questionnaire A system started at T=300K and pressure equal to 1atm, then the following steps were performed on the system isothermally, calculate the heat, work, change in internal energy, change in enthalpy in each case Q1) volume is reduced to half Q2) pressure is doubled Q3) volume is thriced Q4) pressure is taken to 5 atm `

Answers A1) a ,1728.8,0,0 b , ,0,0 c , ,0,0 d ,1728.8,0,0 A2) a ,1728.8,0,0 B ,1728.8,0,0 c , ,0,0 d , ,0,0 A3) a , ,0,0 b ,2740.2,0,0 c , ,0,0 d ,2740.2,0,0 A4) a ,4014.3,0,0 b , ,0,0 c , ,0,0 d ,4014.3,0,0 The order of the answer is as follows heat, work, change in internal energy, change in enthalpy in each case Answers A1) a A2) b A3) c A4) d