Thermodynamic Relations: Interactive Learning Quizzes for Thermodynamics

Question 1

For a closed system undergoing an infinitesimal, reversible process, which of the following equations describes the change in its internal energy?

Accepted Answer

dU = dQ - dW

Answer

dU = dQ

Answer

dU = dW

Answer

dU = 0

Question 2

Identify the equation that does not represent a Maxwell relation:

Accepted Answer

dE = T dS + p dV

Answer

dU = T dS - pdV

Answer

dH = T dS + V dp

Answer

dG = -S dT + V dp

Question 3

In a closed system undergoing a reversible isothermal process, what are the changes in entropy (ΔS) and heat transfer (Q)?

Accepted Answer

ΔS = 0, Q = 0

Answer

ΔS > 0, Q > 0

Answer

ΔS < 0, Q < 0

Answer

ΔS = Q/T

Question 4

A Carnot heat engine operates between two reservoirs at temperatures of 500 Kelvin and 300 Kelvin. Assuming an ideal process, what is the maximum theoretical efficiency of the engine?

Accepted Answer

40%

Answer

15%

Answer

55%

Answer

85%

Question 5

What is the main purpose of the Gibbs equation in thermodynamics?

Accepted Answer

To determine the change in free energy of a system

Answer

To determine the change in entropy of a system

Answer

To determine the change in enthalpy of a system

Answer

To determine the change in internal energy of a system

Question 6

In thermodynamics, what is the defining characteristic of the Gibbs equation?

Accepted Answer

Relates changes in thermodynamic properties to temperature and pressure variations.

Answer

Predicts the behavior of non-equilibrium systems.

Answer

Applies only to systems at equilibrium.

Answer

Has limited practical use in engineering.

Question 7

In the context of closed thermodynamic systems, the Gibbs equation is applicable to which types of systems and what is its primary utility?

Accepted Answer

Both ideal and non-ideal systems; determining equilibrium composition by minimizing Gibbs free energy

Answer

Ideal systems only; determining equilibrium composition

Answer

Open systems only; relating changes in Gibbs free energy to changes in temperature, pressure, and composition

Answer

Ideal closed systems only; determining equilibrium composition

Question 8

Which characteristic distinguishes a thermodynamic system that exchanges both energy and mass with its surroundings?

Accepted Answer

Variable system volume due to mass exchange

Answer

Constant mass

Answer

Isolated from external interactions

Answer

Unchanging energy content

Question 9

A defining characteristic of an open thermodynamic system is the exchange of what with its surroundings?

Accepted Answer

Energy and mass

Answer

Energy

Answer

Work

Answer

Heat

Question 10

In a closed, isothermal, and reversible thermodynamic process, what happens to the internal energy of the system?

Accepted Answer

Remains constant

Answer

Increases

Answer

Decreases

Question 11

In a closed system undergoing a reversible isothermal process, which thermodynamic relation links pressure-volume and entropy-temperature properties?

Accepted Answer

Maxwell relation

Answer

Clausius-Clapeyron equation

Answer

Gibbs equation

Answer

Joule-Thomson coefficient

Question 12

For a closed thermodynamic system that is not in equilibrium, what is the possible range of entropy change (ΔS) during a spontaneous process?

Accepted Answer

ΔS can be either positive or negative, depending on the process and the system's initial and final states.

Answer

ΔS is always positive.

Answer

ΔS is always negative.

Answer

ΔS is always zero.

Question 13

Identify the expression that is not a Maxwell relation:

Accepted Answer

dP = (∂V/∂P)_T dT - (∂V/∂T)_P dP

Answer

dS = (∂U/∂S)_V dT - (∂U/∂T)_S dV

Answer

dG = -SdT + VdP

Answer

dU = TdS - PdV

Question 14

In a fuel cell operating steadily with an efficiency of 70%, what percentage of the energy supplied is released as heat?

Accepted Answer

30%

Answer

10%

Answer

50%

Answer

70%

Question 15

In thermodynamics, which practical application best exemplifies the Gibbs equation's utility?

Accepted Answer

Predicting the spontaneity of chemical reactions

Answer

Determining the work output of an adiabatic process

Answer

Calculating the heat capacity of a substance at constant pressure

Question 16

Which equation is NOT a Maxwell relation?

Accepted Answer

dU = T dS

Answer

dU = T dS - p dV

Answer

dH = T dS + V dp

Answer

dG = -S dT + V dp

Question 17

Which Maxwell relation represents the change in pressure (P) with respect to temperature (T) at constant volume (V)?

Accepted Answer

d(P/T)/dV = (d^2S/dV^2)/T

Answer

d(P/T)/dV = -(d^2U/dV^2)/T

Answer

d(T/P)/dV = (d^2G/dV^2)/T

Answer

d(V/T)/dP = (d^2H/dP^2)/T

Question 18

In a closed system undergoing a reversible process, the infinitesimal work done on the system is equal to:

Accepted Answer

The change in volume multiplied by the negative of the pressure

Answer

The change in internal energy multiplied by the change in volume

Answer

The change in entropy multiplied by the temperature

Answer

Always zero

Question 19

In a closed, reversible system undergoing an isothermal process, how does the entropy change (ΔS) relate to the work done by the system (W)?

Accepted Answer

ΔS = -W/T

Answer

ΔS = W

Answer

ΔS = W/T

Answer

ΔS is independent of W

Question 20

A thermodynamic system undergoes a process from state A to state B, resulting in a decrease in Gibbs free energy. What can you conclude about the spontaneity of the process?

Accepted Answer

Spontaneous

Answer

Irreversible

Answer

Requires external energy input

Answer

Involves heat transfer

Question 21

How can you express the specific heat capacity at constant volume (Cv) using the isothermal compressibility (κT) and a Maxwell relation?

Accepted Answer

Cv = -κT (∂P / ∂T)v

Answer

Cv = κT (P / T)

Answer

Cv = -κT (∂V / ∂P)T

Answer

Cv = κT (T / P)

Question 22

How can the Gibbs equation be used to determine the equilibrium constant of a chemical reaction at constant temperature and pressure?

Accepted Answer

Calculate the change in Gibbs free energy, which is related to the equilibrium constant by ΔG° = -RTlnK.

Answer

Calculate the equilibrium constant directly.

Answer

Calculate the entropy change, which is related to the equilibrium constant by ΔS° = RlnK.

Answer

The Gibbs equation cannot be used to determine the equilibrium constant.

Question 23

In a cyclic process involving isothermal and adiabatic transformations, what is the net change in entropy of the system over one complete cycle, as determined using the Gibbs equation?

Accepted Answer

Zero

Answer

Positive

Answer

Negative

Answer

Dependent on the specific path taken

Question 24

Which example best illustrates the practical application of the Gibbs equation in scientific advancement?

Accepted Answer

Predicting phase transitions in materials

Accepted Answer

Evaluating the stability of chemical reactions

Answer

Improving the efficiency of internal combustion engines

Question 25

In a closed system undergoing a reversible process, when do we observe no change in Gibbs free energy (G)?

Accepted Answer

When both dT and dP are 0

Answer

When dP is less than dV

Answer

When dT is greater than 0 and dP equals 0

Question 26

What is the primary purpose of the Gibbs equation in thermodynamics?

Accepted Answer

Determining changes in Gibbs free energy

Answer

Determining changes in entropy

Answer

Calculating changes in enthalpy

Answer

Determining changes in internal energy

Question 27

For a system undergoing a change from state 1 to state 2 at constant temperature, which statement accurately describes the internal energy change?

Accepted Answer

Change in internal energy is zero.

Answer

Change in enthalpy is zero.

Answer

Change in entropy is zero.

Answer

Work done by the system is zero.

Question 28

Which of the following statements correctly describes a spontaneous process?

Accepted Answer

dG < 0

Answer

dG > 0

Answer

dS = 0

Answer

dU = 0

Question 29

Which of the following is NOT a thermodynamic potential?

Accepted Answer

Pressure

Answer

Internal energy

Answer

Helmholtz free energy

Question 30

What is the physical interpretation of the Maxwell relation (left(rac{partial T}{partial P}ight)_S)?

Accepted Answer

It indicates the rate of temperature change with respect to pressure, keeping entropy constant.

Answer

It shows the relationship between entropy and pressure at a fixed temperature.

Answer

It determines the system's heat capacity.

Question 31

Which of the following is a thermodynamic potential that combines the internal energy, pressure, and temperature of a system?

Accepted Answer

Enthalpy

Answer

Entropy

Answer

Temperature

Answer

Volume

Question 32

In a spontaneous isothermal reaction at equilibrium, how can the Gibbs equation be applied to determine the equilibrium constant (K) of the reaction?

Accepted Answer

$K = exp(-Delta_r G^circ / RT)$

Answer

$K = exp(-Delta_r S^circ / RT)$

Answer

$K = exp(-Delta_r V^circ / RT)$

Question 33

Which of the following expressions represents the Maxwell relation for isothermal compressibility?

Accepted Answer

κT = (∂P/∂V)T

Answer

κT = -(∂V/∂P)S

Answer

αP = (∂V/∂T)P

Answer

αP = -(∂T/∂V)S

Question 34

Given the Gibbs equation, dG = VdP - SdT, what is the partial derivative of G with respect to T at constant pressure?

Accepted Answer

-S

Answer

V

Answer

0

Answer

P

Question 35

Which of the following is NOT a consequence of the second Maxwell relation?

Accepted Answer

The isochoric heat capacity is always positive.

Answer

The isothermal compressibility is positive.

Answer

The isobaric thermal expansion coefficient is positive.

Answer

The isentropic Joule-Thomson coefficient is negative.

Question 36

A system undergoes a process in which its Gibbs free energy increases by 100 J. If the process is carried out at constant temperature, what is the minimum work done by the system?

Accepted Answer

-100 J

Answer

100 J

Answer

0 J

Answer

Insufficient information

Question 37

The Gibbs equation has numerous applications in thermodynamics. Which of the following is NOT one of them?

Accepted Answer

Calculating the enthalpy change of a process

Answer

Calculating the equilibrium constant of a chemical reaction

Answer

Determining if a process will occur spontaneously

Answer

Predicting the direction of a chemical reaction

Question 38

How does the Clausius inequality relate to the efficiency and spontaneity of cyclic processes in thermodynamics?

Accepted Answer

It defines the maximum efficiency of heat engines and predicts the direction of irreversible processes.

Answer

It applies only to reversible processes and stems from the second law of thermodynamics.

Answer

It implies that the entropy change of an isolated system is always positive.

Question 39

How do Maxwell relations contribute to the derivation of the fundamental equation for phase equilibrium, and what insights do they provide into understanding phase transitions?

Accepted Answer

By employing Maxwell relations, we can derive the Gibbs-Duhem equation, which establishes the stability criteria for phase equilibrium and helps predict the direction of phase transitions.

Answer

Maxwell relations are not directly employed to calculate the entropy change during phase transitions.

Answer

Maxwell relations do not directly determine the equilibrium composition of multiphase systems.

Answer

Maxwell relations are inapplicable to phase equilibrium systems.

Question 40

State the Gibbs equation:

Accepted Answer

dG = -SdT + VdP + Σμ_idn_i

Answer

dU = TdS - PdV

Answer

dH = dU + PdV

Question 41

Which of the following is a closed system?

Accepted Answer

A sealed container of gas

Answer

A room with an open window

Answer

A flowing river

Answer

A person breathing

Question 42

Which of the following is an isothermal process?

Accepted Answer

A process that occurs at constant temperature

Answer

A process that occurs at constant entropy

Answer

A process that occurs at constant pressure

Answer

A process that occurs at constant volume

Question 43

Which of the following is a Maxwell relation that relates temperature and entropy at constant volume?

Accepted Answer

(∂T/∂V)s = -(∂P/∂S)v

Answer

(∂U/∂V)t = P

Answer

(∂G/∂P)T = V

Answer

(∂H/∂T)v = Cp

Question 44

Which of the following is NOT a thermodynamic potential?

Accepted Answer

Entropy

Answer

Enthalpy

Answer

Internal energy

Answer

Gibbs free energy

Question 45

A characteristic of a reversible process is that:

Accepted Answer

The system returns to its initial state when the process is reversed.

Answer

The system's entropy decreases.

Answer

The system's internal energy increases.

Question 46

Regarding a closed system, its entropy can:

Accepted Answer

Increase, decrease, or remain constant.

Answer

Only increase.

Answer

Only decrease.

Answer

Always be zero.

Question 47

The Maxwell relation (∂H/∂P)T = V - T(∂V/∂T)P indicates that:

Accepted Answer

Enthalpy is a function of both pressure and temperature.

Answer

Specific volume is independent of temperature.

Answer

Internal energy is a function of volume and temperature.

Question 48

Which application of the Gibbs equation is relevant for calculating the chemical potential of a component in a mixture?

Accepted Answer

$$\mu_i = \left(\frac{\partial G}{partial n_i}ight)_{T,P,n_j
e i}$$

Answer

$$\mu_i = \left(\frac{\partial U}{partial n_i}ight)_{T,V,n_j
e i}$$

Answer

$$\mu_i = \left(\frac{\partial H}{partial n_i}ight)_{T,P,n_j
e i}$$

Question 49

Which of the following is not considered a thermodynamic property?

Accepted Answer

Time

Answer

Entropy

Answer

Temperature

Answer

Pressure

Question 50

Identify the thermodynamic process that maintains constant entropy within the system:

Accepted Answer

Isentropic process

Answer

Isothermal process

Answer

Adiabatic process

Answer

Isobaric process

Question 51

For an ideal gas, what is the relationship between the specific heat at constant volume (Cv) and the specific heat at constant pressure (Cp)?

Accepted Answer

Cp - Cv = R

Answer

Cv - Cp = R

Answer

Cp + Cv = R

Answer

Cp / Cv = R

Question 52

Which condition must be met for a process to be considered isentropic?

Accepted Answer

The process must be both reversible and adiabatic.

Answer

The process must be isochoric and isobaric.

Answer

The process must be isobaric and isothermal.

Answer

The process must be irreversible and adiabatic.

Question 53

During a reversible isothermal process, what is the change in entropy?

Accepted Answer

ΔS = Q/T

Answer

ΔS = T/Q

Answer

ΔS = Q/T0

Answer

ΔS = Q - T

Question 54

Which of the following is NOT a recognized thermodynamic process?

Accepted Answer

Isochronal process

Answer

Isothermal process

Answer

Isobaric process

Answer

Isochoric process

Question 55

What is the significance of the Clausius-Clapeyron equation?

Accepted Answer

It relates pressure and temperature changes during phase transitions.

Answer

It describes the relationship between entropy and temperature.

Answer

It predicts the equilibrium constant for chemical reactions.

Question 56

Which of the following is an extensive property?

Accepted Answer

Volume

Answer

Density

Answer

Temperature

Answer

Pressure

Question 57

The Gibbs equation is employed to determine changes in which thermodynamic property?

Accepted Answer

Gibbs free energy

Answer

Entropy

Answer

Enthalpy

Answer

Internal energy

Question 58

For an isothermal process, what is the relationship between entropy change and heat transfer?

Accepted Answer

ΔS = Q/T

Answer

T = ΔS/Q

Answer

ΔS = T/Q

Answer

Q = ΔS/T

Question 59

From the Gibbs equation, which thermodynamic property can be derived?

Accepted Answer

Enthalpy

Answer

Entropy

Answer

Internal energy

Answer

Volume

Question 60

Identify the central concept in thermodynamic relations.

Accepted Answer

Partial derivatives

Answer

Ideal gas behavior

Answer

Heat transfer modes

Answer

Thermodynamic equilibrium

Question 61

To which systems are Maxwell relations applicable?

Accepted Answer

Closed systems in equilibrium

Answer

Open systems in equilibrium

Answer

Closed systems not in equilibrium

Answer

Open systems not in equilibrium

Question 62

Identify the Maxwell relation that relates heat transfer (dQ) to entropy (dS) and pressure (dV).

Accepted Answer

dQ = T dS - p dV

Answer

dS = dQ/T

Answer

dH = dQ - p dV

Answer

dU = T dS + p dV

Question 63

What is the Gibbs equation, written in terms of Gibbs free energy (dG), temperature (dT), and pressure (dp)?

Accepted Answer

dG = -S dT + V dp

Answer

dS = dQ/T

Answer

dU = T dS - p dV

Answer

dH = T dS + p dV

Question 64

Which type of system is most suitable for analysis using the Gibbs equation?

Accepted Answer

Closed chemical reaction system.

Answer

System in mechanical equilibrium.

Answer

Adiabatically expanding system.

Answer

Open system undergoing heat transfer.