AP Physics Chp 15

Thermodynamics – study of the relationship of heat and work System vs Surroundings Diathermal walls – allow heat to flow through Adiabatic walls – do not allow heat to flow

Zeroth Law of Thermodynamics Two systems in thermal equilibrium with a third are also in equilibrium with each other

First Law of Thermodynamics Internal energy changes based on the amount of heat and/or work done by/on the system. U = Q – W W = PV Q is positive when it goes in (endothermic) W is positive when the system does work

What is the change in the internal energy if you supply 15 kJ to a 35 m 3 sample of helium at Pa and it is allowed to expand to 52 m 3 ?

U = Q – W U = J – ( Pa)(52 m 3 – 35 m 3 ) U =

If a process is slow enough then the P and T are uniform. When P is constant its called an isobaric process. W = PV Why is W negative when work is done on a system?

Isochoric processes occur at constant volume This is the bomb calorimeter idea.

At constant T its an isothermal process Adiabatic processes occur without the transfer of any heat

One way to relate work for a system is to plot the P vs V graph and compare the area under the curve.

How much work is done in compressing the gas from 4 m 3 to 3 m 3 ? Why is it more than 9 m 3 to 8 m 3 ?

What would a graph for an isochoric process look like? Why does it show no work being done?

What about isobaric, hows its graph look and is there any work?

Isothermal process – Expansion or Compression Since T is constant the internal energy is constant so Q = W

Any work done by the gas results in heat flowing out to the surroundings and vice versa.

Adiabatic Processes – Expansion/Compression Since no heat is transferred the internal energy is related only to the work U = -W

When the gas does work the T decreases and the internal energy of the gas has decreased

If 2 moles of an ideal gas expands from to m 3 at a pressure of Pa, how much work is done? W = PV W = Pa(0.050 m m 3 ) W = 3039Pa m 3 = J

If the temperature is allowed/forced to remain constant how has the internal energy changed? 0 U = 3/2 nRT so with no change in T there is no change in internal energy

How much heat was transferred? The same as the work. Q = W Q = 3039 J

What is the temperature of the gas? 3039J = (2n)(8.31J/nK)T ln(0.050/0.020) T = K

Specific Heat Capacities Gases use a molar heat capacity at constant pressure and another for constant volume C p and C v

Ideal Gases At constant pressure the heat is related to both the change in internal energy and work thus C p = 5/2R At constant volume its only the internal energy and C v = 3/2R So C p – C v = R

Isobaric (P const) W = PV Isochoric (V const) W = 0 Isothermal (T const) W = nRT ln(V f /V o ) Adiabatic (no Q) W = 3/2nR(T o – T f )

2 nd Law of Thermodynamics Heat flows spontaneously from a higher temperature to a lower temperature

Heat engines use heat to perform work. – Heat comes from a hot reservoir – Part of the heat is used to perform work – The remainder is rejected to the cold reservoir Efficiencey e = W/Q H

Efficiency can be multiplied by 100 to make it a percentage. Since Q H = W + Q C W = Q H – Q C e = 1 – Q C /Q H

Carnot created a principle that says that a irreversible engine can not have a greater efficiency than a reversible one operating at the same temperatures. For a Carnot engine Q C /Q H = T C /T H e carnot = 1 – T C /T H

If absolute zero could be maintained while depositing heat in then a 100% efficiency would be possible but its not.

If my truck operates at a running temperature of 94 o C and the outside air is only -5 o C, what is the maximum efficiency for the engine?

T H = = 367 K T C = = 268 K e = 1 – T C /T H e = 1 – 268K / 367 K = 0.27 or 27%

Refrigerators, Air Conditioners, Heat Pumps All of these take heat from the cold reservoir and put it into the hot reservoir by doing a certain amount of work. Its the reverse of the heat engine.

Why cant you cool your house by running an air conditioner without having it exhaust outside? Coefficient of performance = Q C /W Heat pumps warm up a space by moving heat from the cold outside to the warm inside.

Seems kind of weird that the cold outside has heat. If you use a Carnot heat pump to deliver 2500 J of heat to your house to achieve a temperature of 20 o C while it is -5 o C outside, how much work is required?

W = Q H – Q C and Q C /Q H = T C /T H So Q C = Q H T C /T H and W = Q H – Q H T C /T H W = Q H (1-T C /T H ) W = 2500J ( K/293K) = 210 J

Entropy Randomness or disorder gas>>>liquids>solids The entropy of the universe increases for irreversible process but stays constant for reversible

Since carnot engines are reversible Q C /T C = Q H /T H Thus

If we set the hot coffee pot at 372K on the table at 297K and they exchange 4700 J of heat, how much has the entropy of the universe changed?

What happens to the energy in irreversible processes? Since the Suniv increases the increase is due to the energy being removed from being able to do any work

W unavailable = T c Suniv So how much energy was lost to do work in the earlier example? Wunav = (295K)(3.3J/K) = 970 J