THERMODYNAMICS Group Carnot on Work and Thermodynamics Process

Sadi Carnot ( ): The "father" of thermodynamics “ We use here motive power (work) to express the useful effect that a motor is capable of producing. This effect can always be likened to the elevation of a weight to a certain height. It has, as we know, as a measure, the product of the weight multiplied by the height to which it is raised.” Work, i.e. "weight lifted through a height", was originally defined in 1824 by Sadi Carnot

WORK In thermodynamics, work is performed whenever a force acts through a distance. By definition, WORK is given by the equation : By convention, where F is the component of force acting along the line of the displacement dl. Work regarded as +ve when the displacement is in the same direction –ve when the displacement is in the opposite direction. In SI, work is measured in joules (J).

Pressure-volume work Chemical thermodynamics studies PV work, which occurs when the volume of a fluid changes. PV work is represented by the following differential equation: where: –W = work done on the system –P = external pressure –V = volume Therefore, we have:

A common type of work associated with a chemical process is the work done by a gas through expansion or the work done to a gas through compression. An example,Combustion of gasoline is used to expand gases in the cylinders of car's engine and push back the pistons. This motion is then translated into the motion of the car. Now remember that work is defined as a Force applied over a distance is –Work = F x Δh,

where Δh = hfinal - hinitial. Thus, the work associated with moving a piston a distance Δh is –Work = p x ΔV, where ΔV = Vfinal – Vinitial,recognizing A x Δh as the change in volume of the cylinder, so –|Work| = p x ΔV. If ΔV is positive then the gas is expanding and doing work on the surroundings. So work should be negative Work = - p x ΔV

CP: Molar Heat Capacity at constant pressure. CV: Molar Heat Capacity at constant volume. CS: Specific Heat Capacity at constant pressure.

Thermodynamic process can be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. pressure-volume is concerned with the transfer of mechanical or dynamic energy as the result of work. The basic properties are: –isobaric process –isochoric process –isothermal process –adiabatic process –isentropic process –isenthalpic process –steady state

Isobaric Process Occurs at constant pressure According to the first law of thermodynamics, where W is work done by the system, U is internal energy, and Q is heat. Pressure-volume work (by the system) is defined as:first law of thermodynamics but since pressure is constant, this means that Applying the ideal gas law, this becomes

assuming that the quantity of gas stays constant (e.g. no phase change during a chemical reaction). Since it is generally true thatphase changechemical reaction then substituting the last two equations into the first equation produces: The quantity in parentheses is equivalent to the molar specific heat for constant pressure:parenthesesspecific heatpressure cp = cV + R

An isobaric process is shown on a P-V diagram as a straight horizontal line, connecting the initial and final thermostatic states. If the process moves towards the right, then it is an expansion. If the process moves towards the left, then it is a compression. The yellow area represents the work done

Isochoric Process called an isometric process or an isovolumetric process, is a thermodynamic process in which the volume stays constant; ΔV = 0. This implies that the process does no pressure-volume work, since such work is defined bythermodynamic processwork ΔW = PΔV where P is pressure (no minus sign; this is work done by the system). By applying the first law of thermodynamics, we can deduce that ΔU the change in the system's internal energy, isfirst law of thermodynamics ΔU = Q

for an isochoric process: all the heat being transferred to the system is added to the system's internal energy, U. If the quantity of gas stays constant, then this increase in energy is proportional to an increase in temperature, Q = nCVΔT where CV is molar specific heat for constant volume. On a P-V diagram, an isochoric process appears as a straight vertical line.P-V diagram

Isothermal Process Occurs at a constant temperature: ΔT = 0 This typically occurs when a system is in contact with an outside thermal reservoir (heat bath), and processes occur slowly enough to allow the system to continually adjust to the temperature of the reservoir through heat exchange.heat bathprocessesheat Consider an ideal gas, in which the temperature depends only on the internal energy, which is a function of the mean translational kinetic energy of the molecules, as given by a Boltzmann distribution; if the internal energy is constant, so is the temperature. Take the number of moles n as a constant.ideal gasinternal energymeankinetic energy moleculesBoltzmann distributionmoles

but this means, according to the ideal gas law, thatideal gas law so that where Pi and Vi are the pressure and volume of the initial state, Pf and Vf are the pressure and volume of the final state, and the variables P and V stand for the pressure and volume of any intermediate state during an isothermal process.variables

Some isotherms of an ideal gasisotherms Curves called isotherms appear as a hyperbolas on a P- V (pressure-volume) diagram (T = constant). Each one asymptotically approaches both the V (abscissa) and P (ordinate) axes. This corresponds to a one-parameter family of curves, a function of T, whose equation ishyperbolas asymptoticallyparameterfunction By the first law of thermodynamics, the isotherms of an ideal gas are also determined by the condition thatfirst law of thermodynamics

where W is work done on the system. (While Q and W are incremental quantities, they do not represent differentials of state functions.) This means that, during an isothermal process, all heat accepted by the system from its surroundings must have its energy entirely converted to work which it performs on the surroundings. That is, all the energy which comes into the system comes back out; the internal energy and thus the temperature of the system remain constant.quantitiesdifferentialsstate functionsenergywork

The yellow area equals work. In a minute process of this process, the minute work dW can be shown as follow. dW = Fdx = PSdx = PdV Therefore the entire work of the process from A to B is shown with the integration of the previous equation. Here, by the ideal gas equation, Therefore in the isothermal process, the following equation is formed.

Adiabatic Process Process in which there is no energy added or subtracted from the system by heating or cooling. For a reversible process, this is identical to an isentropic process. If the system is thermally insulated from its environment, its boundary is a thermal insulator. But if a system has an entropy which has not yet reached its maximum equilibrium value, the entropy will increase even though the system is thermally insulated.

An example of an adiabatic process is a gas expanding so quickly that no heat can be transferred. The expansion does work, and the temperature drops. This is exactly what happens with a carbon dioxide fire extinguisher, with the gas coming out at high pressure and cooling as it expands at atmospheric pressure.

Isentropic Process Occurs at a constant entropy. For a reversible process this is identical to an adiabatic process. If a system has an entropy which has not yet reached its maximum equilibrium value, a process of cooling may be required to maintain that value of entropy.

Isenthalpic Process the thermodynamic potentials may be held constant during a process which means no change in enthalpy in the system.

Steady state Steady state is a more general situation than Dynamic equilibrium. If a system is in steady state then the recently observed behaviors of the system will continue into the future. In stochastic systems, the probabilities that various different states will be repeated will remain constant. In many systems, steady state is not achieved until some time has elapsed after the system is started or initiated. This initial situation is often identified as a transient state, start-up or warm-up period. While a dynamic equilibrium occurs when two or more reversible processes occur at the same rate, and such a system can be said to be in steady state; a system that is in steady state may not necessarily be in a state of dynamic equilibrium, because some of the processes involved are not reversible.