Grade 11 Physics Thermodynamics Quiz (Set 2) - Practice Questions

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Grade 11 : Physics - Thermodynamics (Set 2)— Questions & Detailed Solutions

Two systems A and B are individually found to be in thermal equilibrium with a third system C.
According to the Zeroth Law of Thermodynamics, what can be concluded about systems A and B?

(A)

Systems A and B are in thermal equilibrium with each other.

(B)

System A has double the heat content of system B.

(C)

Work must be done to bring systems A and B to thermal equilibrium.

(D)

Heat spontaneously flows from system A to system B.

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✓ Correct Option: (A)

Explanation: The Zeroth Law of Thermodynamics states that if two bodies A and B are each in thermal equilibrium with a third body C, then A and B are in thermal equilibrium with each other. This law forms the physical basis for the concept of temperature.

A closed thermodynamic system absorbs 500 J of heat from its surroundings while performing 200 J of work on its surroundings.
What is the net change in the internal energy ($\Delta U$) of the system?

(A)

700 J

(B)

300 J

(C)

-300 J

(D)

2.5 J

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✓ Correct Option: (B)

Explanation: By the First Law of Thermodynamics:
$$Q = \Delta U + W$$
Given $Q = +500\text{ J}$ (heat absorbed) and $W = +200\text{ J}$ (work done by system):
$$\Delta U = Q - W = 500\text{ J} - 200\text{ J} = 300\text{ J}$$

A gas is contained in a rigid, fixed-volume container and is heated from 300 K to 400 K.
What is the work done ($W$) by the gas during this isochoric process?

(A)

100 J

(B)

100 kJ

(C)

0 J

(D)

Depends on the initial pressure

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✓ Correct Option: (C)

Explanation: In an isochoric (constant volume) process, the change in volume $\Delta V = 0$.
Since work done is given by $W = \int P \, dV$, when $dV = 0$, the work done is strictly zero ($W = 0\text{ J}$).

A gas expands isobarically at a constant pressure of 100 kPa from an initial volume of $2m^3$ to a final volume of $5m^3$.
Calculate the work done by the gas during expansion.

(A)

300 kJ

(B)

500 kJ

(C)

200 kJ

(D)

150 kJ

View Correct Answer & Detailed Solution

✓ Correct Option: (A)

Explanation: For an isobaric (constant pressure) process, work done is:
$$W = P \Delta V = P(V_f - V_i)$$
Substituting values:
$$W = (100 \times 10^3\text{ Pa}) \times (5\text{ m}^3 - 2\text{ m}^3) = 100 \times 10^3 \times 3 = 300,000\text{ J} = 300\text{ kJ}$$

For an ideal gas, internal energy ($U$) depends solely on which thermodynamic state variable?

(A)

Pressure only

(B)

Temperature only

(C)

Volume only

(D)

Ratio of pressure to volume

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✓ Correct Option: (B)

Explanation: According to Joule's law for an ideal gas, inter-molecular potential energy is zero. Thus, internal energy consists only of kinetic energy, which depends exclusively on the absolute temperature ($T$). Therefore, $U = f(T)$.

Which equation correctly represents Mayer's relation between molar specific heat capacity at constant pressure ($C_p$) and at constant volume ($C_v$) for an ideal gas?

(A)

$C_p - C_v = R$

(B)

$C_v - C_p = R$

(C)

$C_p + C_v = R$

(D)

$C_p / C_v = R$

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✓ Correct Option: (A)

Explanation: Mayer's relation states that the molar heat capacity at constant pressure is greater than at constant volume by the universal gas constant $R$, due to work done during expansion at constant pressure. Hence, $C_p - C_v = R$.

A thermal system undergoes an adiabatic process where no heat is transferred into or out of the system ($Q = 0$).
Which relationship correctly links change in internal energy ($\Delta U$) and work done ($W$)?

(A)

$\Delta U = W$

(B)

$\Delta U = 0$

(C)

$\Delta U = -W$

(D)

$W = 0$

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: In an adiabatic process, heat exchange $Q = 0$.
Applying the First Law of Thermodynamics ($Q = \Delta U + W$):
$$0 = \Delta U + W \implies \Delta U = -W$$

A Carnot engine operates between a hot reservoir at $T_H = 600\text{ K}$ and a cold reservoir at $T_C = 300\text{ K}$.
What is the maximum theoretical efficiency ($\eta$) of this Carnot engine?

(A)

25%

(B)

50%

(C)

75%

(D)

100%

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Efficiency of a Carnot engine is given by:
$$\eta = 1 - \frac{T_C}{T_H}$$
Substituting absolute temperatures:
$$\eta = 1 - \frac{300}{600} = 1 - 0.5 = 0.5\text{ or } 50\%$$

An ideal gas is taken through a complete closed thermodynamic cycle, returning to its initial state.
What is the net change in internal energy ($\Delta U_{net}$) over one full cycle?

(A)

Greater than heat supplied

(B)

Equal to total work done

(C)

Equal to heat added

(D)

Zero

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✓ Correct Option: (D)

Explanation: Internal energy $U$ is a state function depending only on the state of the system. For any cyclic process, the initial state equals the final state, so $\Delta U_{net} = U_{final} - U_{initial} = 0$.

Q10

What is the ratio of specific heat capacities ($\gamma = C_p / C_v$) for an ideal monatomic gas?

(A)

$\frac{5}{3}$

(B)

$\frac{7}{5}$

(C)

$\frac{4}{3}$

(D)

$\frac{3}{2}$

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✓ Correct Option: (A)

Explanation: For an ideal monatomic gas, $C_v = \frac{3}{2}R$ and $C_p = C_v + R = \frac{5}{2}R$.
Therefore, the ratio of specific heats is:
$$\gamma = \frac{C_p}{C_v} = \frac{\frac{5}{2}R}{\frac{3}{2}R} = \frac{5}{3} \approx 1.67$$

Q11

A heat engine absorbs 1000 J of heat energy from a hot reservoir and exhausts 400 J of heat to a cold reservoir during each cycle.
How much work is done by the engine in one cycle?

(A)

1400 J

(B)

1000 J

(C)

600 J

(D)

400 J

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: Energy conservation in a heat engine yields:
$$W = Q_H - Q_C$$
where $Q_H = 1000\text{ J}$ is heat absorbed and $Q_C = 400\text{ J}$ is heat rejected.
$$W = 1000\text{ J} - 400\text{ J} = 600\text{ J}$$

Q12

A refrigerator extracts 400 J of heat from its cold inner chamber while requiring 100 J of electrical work input per cycle.
What is the Coefficient of Performance (COP, $\beta$) of the refrigerator?

(A)

0.25

(B)

4.0

(C)

3.0

(D)

5.0

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: The Coefficient of Performance (COP) of a refrigerator is given by:
$$\beta = \frac{Q_C}{W}$$
Given $Q_C = 400\text{ J}$ and $W = 100\text{ J}$:
$$\beta = \frac{400\text{ J}}{100\text{ J}} = 4.0$$

Q13

An ideal gas undergoes an isothermal expansion at constant temperature $T$.
How does the heat added ($Q$) to the gas compare to the work done ($W$) by the gas?

(A)

$Q = W$

(B)

$Q = 0$

(C)

$Q = -W$

(D)

$W = 0$

View Correct Answer & Detailed Solution

✓ Correct Option: (A)

Explanation: In an isothermal process for an ideal gas, temperature remains constant ($\Delta T = 0$), so internal energy change $\Delta U = 0$.
By the First Law ($Q = \Delta U + W$):
$$Q = 0 + W \implies Q = W$$

Q14

Comparing curves on a P-V diagram passing through the same initial state point $(P_1, V_1)$.
How does the magnitude of the slope of an adiabatic curve compare to the slope of an isothermal curve?

(A)

Adiabatic slope is smaller than isothermal slope

(B)

Adiabatic slope is $\gamma$ times steeper than isothermal slope

(C)

Both slopes are identical

(D)

Adiabatic slope is zero

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✓ Correct Option: (B)

Explanation: Isothermal slope is $\left(\frac{dP}{dV}\right)_{iso} = -\frac{P}{V}$.
Adiabatic slope is $\left(\frac{dP}{dV}\right)_{adia} = -\gamma \frac{P}{V}$.
Since $\gamma > 1$, the adiabatic curve is steeper by a factor of $\gamma$.

Q15

A cyclic process is plotted on a Pressure vs Volume (P-V) graph forming a closed loop.
What physical quantity is represented by the area enclosed by the closed loop on the P-V diagram?

(A)

Change in internal energy

(B)

Total temperature variation

(C)

Net work done during the cycle

(D)

Total mass of the gas

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✓ Correct Option: (C)

Explanation: Work done during each path on a P-V diagram is the area under the curve ($W = \int P\, dV$). For a closed loop, the area inside the loop represents the net work done by/on the system during one complete cycle.

Q16

A sample of 2 moles of an ideal monatomic gas ($C_v = 1.5 R$) is heated at constant volume, raising its temperature by $\Delta T = 20\text{ K}$. Given $R = 8.314\text{ J/(mol K)}$.
How much heat energy is transferred to the gas?

(A)

498.84 J

(B)

249.42 J

(C)

831.40 J

(D)

166.28 J

View Correct Answer & Detailed Solution

✓ Correct Option: (A)

Explanation: At constant volume, heat transferred is given by:
$$Q = n C_v \Delta T = n \left(\frac{3}{2} R\right) \Delta T$$
$$Q = 2 \times 1.5 \times 8.314 \times 20 = 498.84\text{ J}$$

Q17

Which statement correctly reflects the Clausius statement of the Second Law of Thermodynamics?

(A)

Heat can spontaneously flow from a colder body to a warmer body without external work.

(B)

No engine can convert work into heat with 100% efficiency.

(C)

Heat cannot spontaneously flow from a colder body to a hotter body without external work.

(D)

Total energy of the universe is constantly decreasing.

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✓ Correct Option: (C)

Explanation: Clausius statement of the Second Law specifies that it is impossible to construct a device operating in a cycle that produces no effect other than the transfer of heat from a cooler body to a hotter body. External work input is mandatory.

Q18

An ideal gas expands freely into an evacuated insulated container (free expansion).
What happens to the work done ($W$), heat transferred ($Q$), and temperature change ($\Delta T$) during free expansion?

(A)

$W > 0, Q = 0, \Delta T > 0$

(B)

$W = 0, Q > 0, \Delta T < 0$

(C)

$W > 0, Q > 0, \Delta T = 0$

(D)

$W = 0, Q = 0, \Delta T = 0$

View Correct Answer & Detailed Solution

✓ Correct Option: (D)

Explanation: Free expansion into vacuum means opposing pressure is zero, so $W = 0$. The container is insulated, so $Q = 0$. Thus $\Delta U = Q - W = 0$. For an ideal gas, since $\Delta U = 0$, temperature change $\Delta T = 0$.

Q19

A thermodynamic process is defined as quasi-static and reversible if:

(A)

It proceeds infinitely slowly through equilibrium states with no dissipative forces.

(B)

It occurs extremely rapidly so heat cannot escape.

(C)

Friction converts mechanical energy completely into heat.

(D)

The system remains strictly at absolute zero temperature throughout.

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✓ Correct Option: (A)

Explanation: A reversible process must be quasi-static (carried out infinitely slowly so system stays in thermal equilibrium at every moment) and completely free from dissipative forces like friction, viscosity, or electrical resistance.

Q20

A heat transfer of 600 J occurs reversibly to a system maintained at a constant absolute temperature of 300 K.
What is the change in entropy ($\Delta S$) of the system?

(A)

0.5 J/K

(B)

2.0 J/K

(C)

1800 J/K

(D)

300 J/K

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Change in entropy for an isothermal reversible process is calculated as:
$$\Delta S = \frac{Q_{rev}}{T}$$
Substituting values:
$$\Delta S = \frac{600\text{ J}}{300\text{ K}} = 2.0\text{ J/K}$$

grade 11physicsthermodynamicsheat and temperaturecarnot enginelaws of thermodynamics

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Grade 11 : Physics - Thermodynamics (Set 2)

Grade 11 : Physics - Thermodynamics (Set 2)— Questions & Detailed Solutions

Two systems A and B are individually found to be in thermal equilibrium with a third system C.According to the Zeroth Law of Thermodynamics, what can be concluded about systems A and B?

A closed thermodynamic system absorbs 500 J of heat from its surroundings while performing 200 J of work on its surroundings.What is the net change in the internal energy ($\Delta U$) of the system?

A gas is contained in a rigid, fixed-volume container and is heated from 300 K to 400 K.What is the work done ($W$) by the gas during this isochoric process?

A gas expands isobarically at a constant pressure of 100 kPa from an initial volume of $2m^3$ to a final volume of $5m^3$.Calculate the work done by the gas during expansion.

For an ideal gas, internal energy ($U$) depends solely on which thermodynamic state variable?

Which equation correctly represents Mayer's relation between molar specific heat capacity at constant pressure ($C_p$) and at constant volume ($C_v$) for an ideal gas?

A thermal system undergoes an adiabatic process where no heat is transferred into or out of the system ($Q = 0$).Which relationship correctly links change in internal energy ($\Delta U$) and work done ($W$)?

A Carnot engine operates between a hot reservoir at $T_H = 600\text{ K}$ and a cold reservoir at $T_C = 300\text{ K}$.What is the maximum theoretical efficiency ($\eta$) of this Carnot engine?

An ideal gas is taken through a complete closed thermodynamic cycle, returning to its initial state.What is the net change in internal energy ($\Delta U_{net}$) over one full cycle?

What is the ratio of specific heat capacities ($\gamma = C_p / C_v$) for an ideal monatomic gas?

A heat engine absorbs 1000 J of heat energy from a hot reservoir and exhausts 400 J of heat to a cold reservoir during each cycle.How much work is done by the engine in one cycle?

A refrigerator extracts 400 J of heat from its cold inner chamber while requiring 100 J of electrical work input per cycle.What is the Coefficient of Performance (COP, $\beta$) of the refrigerator?

An ideal gas undergoes an isothermal expansion at constant temperature $T$.How does the heat added ($Q$) to the gas compare to the work done ($W$) by the gas?

Comparing curves on a P-V diagram passing through the same initial state point $(P_1, V_1)$.How does the magnitude of the slope of an adiabatic curve compare to the slope of an isothermal curve?

A cyclic process is plotted on a Pressure vs Volume (P-V) graph forming a closed loop.What physical quantity is represented by the area enclosed by the closed loop on the P-V diagram?

A sample of 2 moles of an ideal monatomic gas ($C_v = 1.5 R$) is heated at constant volume, raising its temperature by $\Delta T = 20\text{ K}$. Given $R = 8.314\text{ J/(mol K)}$.How much heat energy is transferred to the gas?

Which statement correctly reflects the Clausius statement of the Second Law of Thermodynamics?

An ideal gas expands freely into an evacuated insulated container (free expansion).What happens to the work done ($W$), heat transferred ($Q$), and temperature change ($\Delta T$) during free expansion?

A thermodynamic process is defined as quasi-static and reversible if:

A heat transfer of 600 J occurs reversibly to a system maintained at a constant absolute temperature of 300 K.What is the change in entropy ($\Delta S$) of the system?

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Two systems A and B are individually found to be in thermal equilibrium with a third system C.
According to the Zeroth Law of Thermodynamics, what can be concluded about systems A and B?

A closed thermodynamic system absorbs 500 J of heat from its surroundings while performing 200 J of work on its surroundings.
What is the net change in the internal energy ($\Delta U$) of the system?

A gas is contained in a rigid, fixed-volume container and is heated from 300 K to 400 K.
What is the work done ($W$) by the gas during this isochoric process?

A gas expands isobarically at a constant pressure of 100 kPa from an initial volume of $2m^3$ to a final volume of $5m^3$.
Calculate the work done by the gas during expansion.

A thermal system undergoes an adiabatic process where no heat is transferred into or out of the system ($Q = 0$).
Which relationship correctly links change in internal energy ($\Delta U$) and work done ($W$)?

A Carnot engine operates between a hot reservoir at $T_H = 600\text{ K}$ and a cold reservoir at $T_C = 300\text{ K}$.
What is the maximum theoretical efficiency ($\eta$) of this Carnot engine?

An ideal gas is taken through a complete closed thermodynamic cycle, returning to its initial state.
What is the net change in internal energy ($\Delta U_{net}$) over one full cycle?

A heat engine absorbs 1000 J of heat energy from a hot reservoir and exhausts 400 J of heat to a cold reservoir during each cycle.
How much work is done by the engine in one cycle?

A refrigerator extracts 400 J of heat from its cold inner chamber while requiring 100 J of electrical work input per cycle.
What is the Coefficient of Performance (COP, $\beta$) of the refrigerator?

An ideal gas undergoes an isothermal expansion at constant temperature $T$.
How does the heat added ($Q$) to the gas compare to the work done ($W$) by the gas?

Comparing curves on a P-V diagram passing through the same initial state point $(P_1, V_1)$.
How does the magnitude of the slope of an adiabatic curve compare to the slope of an isothermal curve?

A cyclic process is plotted on a Pressure vs Volume (P-V) graph forming a closed loop.
What physical quantity is represented by the area enclosed by the closed loop on the P-V diagram?

A sample of 2 moles of an ideal monatomic gas ($C_v = 1.5 R$) is heated at constant volume, raising its temperature by $\Delta T = 20\text{ K}$. Given $R = 8.314\text{ J/(mol K)}$.
How much heat energy is transferred to the gas?

An ideal gas expands freely into an evacuated insulated container (free expansion).
What happens to the work done ($W$), heat transferred ($Q$), and temperature change ($\Delta T$) during free expansion?

A heat transfer of 600 J occurs reversibly to a system maintained at a constant absolute temperature of 300 K.
What is the change in entropy ($\Delta S$) of the system?