Thermodynamics Chapter-Wise Test 11

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A gas at \( 4 \, \text{atm} \) and \( 27^\circ \text{C} \) in a \( 3 \, \text{L} \) container is cooled isochorically to \( -73^\circ \text{C} \). What is the final pressure?

For isochoric: \( \frac{P_1}{T_1} = \frac{P_2}{T_2} \).

\( P_1 = 4 \, \text{atm} \), \( T_1 = 27 + 273 = 300 \, \text{K} \), \( T_2 = -73 + 273 = 200 \, \text{K} \).

\( \frac{4}{300} = \frac{P_2}{200} \Rightarrow P_2 = \frac{4 \times 200}{300} = \frac{8}{3} \approx 2.67 \, \text{atm} \).

2.0 atm
2.67 atm
3.0 atm
3.5 atm
2

What characteristic of a solid’s molecular structure leads to a molar specific heat capacity of approximately \( 3R \)?

In solids, each atom vibrates with 3 degrees of freedom, contributing \( 3 k_B T \) (kinetic and potential) per atom. For a mole, this totals \( 3 R T \), so \( C = \frac{\Delta U}{\Delta T} = 3R \), due to vibrational motion.

Translational motion
Rotational motion
Vibrational degrees of freedom
Intermolecular forces
3

Which of the following is a consequence of the Second Law of Thermodynamics?

The Second Law implies that heat engines cannot convert all absorbed heat into work (Kelvin-Planck), limiting efficiency to less than 100%. This is a fundamental constraint on energy conversion processes.

Energy is always conserved
Efficiency is less than 100%
Temperature remains constant
Work equals heat supplied
2

Which of the following statements is correct about specific heat capacity?

Specific heat capacity (\( s = \frac{\Delta Q}{m \Delta T} \)) measures heat required per unit mass to raise temperature, depending on the substance and conditions (e.g., \( C_p \) vs. \( C_v \)). Option B is correct.

It is the same for all substances
It varies with substance and conditions
It is a state variable
It equals work done per unit mass
2

A system releases \( 550 \, \text{J} \) of heat and performs \( 200 \, \text{J} \) of work. What is the change in internal energy?

First Law: \( \Delta Q = \Delta U + \Delta W \).

\( \Delta Q = -550 \) (heat released), \( \Delta W = 200 \) (work by system).

\( -550 = \Delta U + 200 \Rightarrow \Delta U = -550 - 200 = -750 \, \text{J} \).

-800 J
-750 J
-700 J
-650 J
2

What is the key characteristic of a thermodynamic equilibrium state?

A system in thermodynamic equilibrium has constant macroscopic variables (e.g., pressure, volume, temperature) over time, indicating no net changes or flows within the system or with its surroundings.

Rapid changes in pressure
Constant macroscopic variables
Continuous heat flow
Variable temperature
2

A solid has a molar specific heat capacity of \( 24.9 \, \text{J mol}^{-1} \text{K}^{-1} \). Which element could it be?

Tungsten has \( C = 24.9 \, \text{J mol}^{-1} \text{K}^{-1} \).

Aluminium
Copper
Silver
Tungsten
4

In an isobaric process, \( 2 \, \text{moles} \) of an ideal gas expand from \( 10 \, \text{L} \) to \( 20 \, \text{L} \) at \( 400 \, \text{K} \). What is the work done by the gas? (Take \( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \))

Work done: \( W = P \Delta V = \mu R T \left(\frac{\Delta V}{V_1}\right) \), but directly, \( W = \mu R \Delta T \).

Here, \( \Delta V = 20 - 10 = 10 \, \text{L} \), use \( W = P \Delta V = \mu R T \frac{\Delta V}{V} \), but since \( P V = \mu R T \), \( W = \mu R T \left(\frac{V_2 - V_1}{V_1}\right) \) simplifies via \( P \).

Actually, \( W = \mu R T \left(\frac{V_2}{V_1} - 1\right) \), but directly: \( W = P \Delta V \), and \( P V = \mu R T \).

Correctly, \( W = \mu R \Delta T \), but here \( T \) is constant, so \( W = P \Delta V \), and \( P = \frac{\mu R T}{V} \).

Better: \( W = \mu R T \left(\frac{V_2 - V_1}{V_1}\right) \), no, simply \( W = P \Delta V \), use \( \mu R T \).

\( W = 2 \times 8.3 \times 400 \times \frac{10}{10} = 6640 \, \text{J} \) (corrected via \( P \Delta V \)).

Final: \( W = 2 \times 8.3 \times 400 = 6640 \, \text{J} \) (adjust units if needed, assume \( \Delta V \) in appropriate form).

3320 J
6640 J
9960 J
13280 J
2

What is the molar specific heat capacity at constant volume for a monatomic ideal gas? (Take \( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \))

For a monatomic gas, \( C_v = \frac{3}{2} R \).

\( C_v = \frac{3}{2} \times 8.3 = 12.45 \, \text{J mol}^{-1} \text{K}^{-1} \).

8.3 J mol⁻¹ K⁻¹
12.45 J mol⁻¹ K⁻¹
16.6 J mol⁻¹ K⁻¹
20.8 J mol⁻¹ K⁻¹
2

A system in a cyclic process absorbs \( 860 \, \text{J} \) of heat and performs \( 340 \, \text{J} \) of work. What is the heat rejected?

For cyclic: \( \Delta U = 0 \), \( Q_{\text{net}} = W \).

\( Q_{\text{absorb}} - Q_{\text{reject}} = W \).

\( 860 - Q_{\text{reject}} = 340 \Rightarrow Q_{\text{reject}} = 860 - 340 = 520 \, \text{J} \).

480 J
520 J
560 J
600 J
2

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