Physics II

Question 1

What is an isobaric process?

Answer 1

An isobaric process is a prcoess that takes place at constant pressure.

Question 1

The efficiency of a Carnot engine operating between two heat resevoirs and using an ideal gas as the working fluid is given by:

ε = (T_H - T_C)/T_H

What is the efficiency if the working fluid is some other non-ideal gas?

Answer 1

The efficiency is the same, regardless of the working fluid.

Question 2

What is the difference between a reversible process and an an irreversible process?

Answer 2

A reversible process takes place slowly, so that the system is not taken out of equilibrium.

An irriversible process takes place quickly, so that the system us taken out of equilibrium.

(A truly reversible process would take place in an infinite ammount of time)

Question 2

For an ideal gas, find an expression for the following quantity:

( ∂P/ ∂T)_V

Answer 2

nR/V

Question 3

True or False?

The entropy of the universe always increases when a process occurs; it never decreases.

Answer 3

True. Entropy of the universe increases when a spontaneous process occurs, but spontaneous processes are the only processes that occur. Hence the entropy of the universe always increases.

Question 3

What is special about the change in state function called enthalpy?

ΔH

Answer 3

For a process teking place at constant pressure, the change in enthalpy gives the heat added to the system.

ΔH = Q

Question 4

Who investigated the properties of gases and found that at constant pressure, the volume is proportional to the temperature?

Answer 4

Jacques Charles, 1787

Question 5

Who investigated the properties of gases and found that at constant temperature the pressure is inversely proportional to the volume?

Answer 5

Robert Boyle, 1662

Question 6

What is the relation between P and V for a reversible adiabatic expansion of an ideal gas?

Answer 6

P = const./V^γ

Where the exopnent is:

γ = C_P/C_V

Question 7

What is the efficiency of a Carnot cycle running between a hot resevoir at T_H and a cold resevoir at T_C?

Answer 7

ε = (T_H - T_C)/T_H

Question 7

What is the heat capacity at constant volume for an ideal gas consisting of diatmic molecules?

Answer 7

C_v = 5/2 (nR)

Question 8

The first law is said to be a postulate consisting of two parts. What are these two parts?

Answer 8

The first postulate of the first law is our postulate that the energy of the universe never changes.

The second part of the first law is the postulate that energy U is a state function.

Question 9

What four ssteps make up the thermoynamic cycle of the Stirling engine?

Answer 9

1) Isothermal (Constant Temperature) expansion at T_H,
2) Isochoric (Constant Volume) cooling to T_C,
3) Isothermal compression at T_C,
4) Isothermal heaing back to T_H

Question 9

What postulate concerning energy forms the basis of the First Law of Thermodynamics?

Answer 9

The energy of the universe remains constant.

Question 11

What four steps make up the thermodynamic cycle of the Carnot engine?

Answer 11

1) Isothermal reversible expansion at T_H
2) Adiabatic reversible expansion to lower the temperature to T_C
3) Isothermal reversible compression at T_C
4) Adiabatic reversible compression to raise the temperature back to T_H

Question 13

Who showed that the energy of an dieal gas depends only on its temperature? THey also measured the dependance of U with V for real gases.

Answer 13

James Joule and William Thomson (later to be Lord Kelvin)

Question 15

The surroundings are always assumed to take on heat (or give off heat) in a reversible fashion. Why?

Answer 15

The srroundings is the
“rest of the universe”, an infinite resevoir. Thus when any finite ammount of heat from the system is spread throughout the surroundings, the perturbation to the state of the surroundings is negligible. Hence the surroundings remain in equilibrium.

Question 16

True or False?

The state of a system is entirely determined by the specification of just two state variables.

Answer 16

True.

For example, if you specify V and T for an ideal gas, then you can figure out P from the equation of state.

You can also figure out U since U is

C_V * T

(We are assuming that the number of moles of gas is known)

Question 18

What is important about the change in state function called internal energy?

ΔU

Answer 18

For a process taking place at constant colume, the change in the energy is equal to the heat added to the system
.

ΔU = Q

Question 18

Reversible work is performed when the difference between the pressure of the system and the presure of the surroundings is infitessimal.

What is the analogous requirement on temperature so that heat is transferred reversibly?

Answer 18

There should be an infitessimal difference between the temperature of the system and the temperature of the surrounding in order to keep the system in equilibrium.

(The surroundings always stays in equilibrium because of its vast size)

Question 19

What is the relation between the heat capacity at constant pressure and the heat capacity at constant volume for an ideal gas?

Answer 19

C_P = C_V + nR

Question 20

What convention do we follow?

a) Q the heat added to the system from the surroundings

or

b) Q the heat passed to the surroundings from the system

Answer 20

a) Q is the heat added to the system frim the surroundings.

Thus Q is positive if the heat is transferred to the system from the surroundings, and Q is negative if the heat is transferred from the system to the surroundings.

Question 21

What convention do we follow?

a) W the work done on the system by the surroundings

or

b) W the work done on the surroundings by the system

Answer 21

b)

Our convention is that W is the work done on the surroundings by the system.

If the system does work on the surroundings, W is positive. If the surroundings do work on the system, W is negative

Question 22

What is the connection between an irreversible process and a spontaneous process

Answer 22

All spontaneous prcess, i.e. processes that occur in a finite ammount of time, require an imalance of forces. They are therefore irreversible processes.

Question 24

True or False? It can be proved that the heat capacity at constant pressure is greater thean the heat capacity at constant volume regardless of the substance.

Answer 24

True

Question 25

In thermodynamics we talk about the system and the surroundings. What is the system? What is the surroundings?

Answer 25

The system is that part of the universe on which we are focusing our attention. The surroundings is the rest of the universe.

Question 26

The energy of a certain real (non-ideal) gas is given by U = 3/2 (nRT) - a(n²/V²) What is the heat capacity at constant volume?

Answer 26

Answer: C_v = (∂U/∂T)_V = 3/2(nR)

Question 28

True or False? The entropy of S is a state function. It is sometimes related to heat, and sometimes not realated to heat. It is related to heat when heat is transferred reversibly.

Answer 28

True.

Question 29

The energy of a certain real (non-ideal) gas is given by U = 3/2 (nRT) - a (n²/V²) The equation of state for the gas is Pv = nRT - a (n²/V²) Find the enthalpy H(T,V) as a function of T and V

Answer 29

Answer: Remember the definition H = U + PV H = U + PV = 5/2 (nRT) - 2a (n²/V)

Question 30

The energy of a certain real (non-ideal) gas is given by U = (3/2)nRT - a (n²/V) Calculate the coefficients of expansion of U(T,V) in the variables T anad V.

Answer 30

Answer: ∂U = (∂U/∂T)_V dT + (∂U/∂V)_T dV (∂U/∂T)_V = 3/2 (nR) (∂U/∂V)_T = a(n²/V²)

Question 31

What mathematical relation is reagarded as a formal statement of the first law of thermodynamics?

Answer 31

ΔU = Q - W

Question 32

Who is credited with figuring out the second law of thermodynamics?

Answer 32

Rudolph Clausius, 1850

Question 33

Who devised a hypothetical heat engine that could be run reversibly between two heat, one resevoirs kept at a hot temperature and the other at a cold temperature?

Answer 33

Sadi Carnot, 1820

Question 34

What is an adiabatic process?

Answer 34

This is a process that takes place in an insulated contianer so that no heat is exchanged with the surroundings.

Question 35

Who patented a heat engine in 1816, for the purpose of powering underwater torpedos without leabing a trail of bubbles?

Answer 35

Robert Stirling, 1816

Question 36

True or False? The energy of an ideal gas is given by the following expression: U = C_V \* T

Answer 36

True. The energy og an ideal gas is a function of temerature only. Since the derivative of U with respect to T is equal to C_V it follows that C_V is the proportionality constant between U and T

Question 37

A system consists of an ice cube. It is initially at a temperature of 270 K and a pressure of 1 atm. It melts, becoming water at 294 K and a pressure of 1 atm. True or False? The change in the entropy of the ststem depends on whether the melting takes place slowly or quickly.

Answer 37

False. Entropy is a state function so the change in S only dpeends on the final and initial states. It does not depend on the path taken to go from one state to the other.

Question 38

What is an isochoric process?

Answer 38

An isochoric process is a process that takes place at constant volume.

Question 39

True or False? If a piston expands irreversibly, it is impossible to calculate the work because it is impossible to dtermine the integral ∫PdV because we have no way out of assigning P to a system out of equilibrium.

Answer 39

False. Even if we can't define the equilibrium pressure of the gas, we can still measrue the extermal pressure on the piston as a function of volume, in principle. The work is the integral ∫P_ext dV

Question 40

True or False? The entropy of a system always increases when a process occurs spontaneously.

Answer 40

False. It is the sum of the entropy of the system plus the entropy of the surroundings that always increases for a spontaneous process, i.e. the entropy of the universe always increases.

Question 41

What is an isothermal process?

Answer 41

This is a process that takes place at constant temperature. What this means is that the final temperature of the system is equal to the initial temperature of the system.

Question 42

True or False? All reversible heat engines operating between two heat resevoirs have the same efficiency?

Answer 42

True, they all have the same efficiency, regardless of the working fluid. The efficiency is the Carnot efficiency. ε = (T_H - T_C)/T_H (The only reversible engine we can imagine is the Carnot engine)