Thermodynamics Chapter-Wise Test 13

Correct answer Carries: 4.

Wrong Answer Carries: -1.

Which of the following statements is correct about internal energy?

Internal energy (\( U \)) is a state function, dependent on the system’s state (e.g., temperature for an ideal gas), not the path taken. Option A is correct.

It is a state function
It depends on the path taken
It is always zero
It measures heat flow
1

A gas undergoes an adiabatic compression with 400 J of work done on it. What is the change in internal energy?

Adiabatic: \( \Delta Q = 0 \), \( \Delta U = -\Delta W \). Work on system: \( \Delta W = -400 \, \text{J} \). \( \Delta U = -(-400) = 400 \, \text{J} \).

350 J
400 J
450 J
500 J
2

A gas at 3 atm in a 4 L container is heated from 25°C to 75°C at constant volume. What is the final pressure?

Isochoric: \( \frac{P_1}{T_1} = \frac{P_2}{T_2} \). \( P_1 = 3 \, \text{atm} \), \( T_1 = 25 + 273 = 298 \, \text{K} \), \( T_2 = 75 + 273 = 348 \, \text{K} \). \( \frac{3}{298} = \frac{P_2}{348} \Rightarrow P_2 = \frac{3 \times 348}{298} \approx 3.5 \, \text{atm} \).

3.0 atm
3.5 atm
4.0 atm
4.5 atm
2

A gas expands adiabatically from \( 5 \, \text{L} \) to \( 20 \, \text{L} \), reducing its temperature from \( 500 \, \text{K} \) to \( 250 \, \text{K} \). If \( 1 \, \text{mole} \) of gas is used and \( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \), what is the work done by the gas? (\( \gamma = 1.5 \))

For adiabatic process: \( W = \frac{\mu R (T_1 - T_2)}{\gamma - 1} \).

\( \mu = 1 \), \( R = 8.3 \), \( T_1 = 500 \), \( T_2 = 250 \), \( \gamma = 1.5 \).

\( W = \frac{1 \times 8.3 \times (500 - 250)}{1.5 - 1} = \frac{8.3 \times 250}{0.5} = 4150 \, \text{J} \).

3000 J
3500 J
4150 J
4500 J
3

A system in a cyclic process absorbs \( 650 \, \text{J} \) of heat and performs \( 200 \, \text{J} \) of work. What is the heat rejected?

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

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

\( 650 - Q_{\text{reject}} = 200 \Rightarrow Q_{\text{reject}} = 650 - 200 = 450 \, \text{J} \).

400 J
450 J
500 J
550 J
2

A system absorbs \( 830 \, \text{J} \) of heat and has \( 290 \, \text{J} \) of work done on it. What is the change in internal energy?

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

\( \Delta Q = 830 \), \( \Delta W = -290 \) (work on system).

\( 830 = \Delta U - 290 \Rightarrow \Delta U = 830 + 290 = 1120 \, \text{J} \).

1000 J
1120 J
1200 J
1300 J
2

An ideal gas absorbs \( 1000 \, \text{J} \) of heat in an isochoric process, increasing its temperature by \( 20 \, \text{K} \). What is the number of moles of the gas? (\( C_v = 20 \, \text{J mol}^{-1} \text{K}^{-1} \))

For isochoric process: \( \Delta Q = \mu C_v \Delta T \).

\( \Delta Q = 1000 \), \( C_v = 20 \), \( \Delta T = 20 \).

\( 1000 = \mu \times 20 \times 20 \Rightarrow \mu = \frac{1000}{400} = 2.5 \, \text{moles} \).

1.5 moles
2.0 moles
2.5 moles
3.0 moles
3

A gas undergoes an adiabatic expansion, doing 450 J of work. What is the change in its internal energy?

Adiabatic: \( \Delta Q = 0 \), \( \Delta U = -\Delta W \). Work by gas: \( \Delta W = 450 \, \text{J} \). \( \Delta U = -450 \, \text{J} \) (internal energy decreases).

-500 J
-450 J
-400 J
-350 J
2

Which of the following is NOT a state variable in thermodynamics?

State variables depend only on the current state of the system, not the path taken to reach it. Pressure, volume, and temperature are state variables. Heat (\( \Delta Q \)) is not a state variable; it is a mode of energy transfer dependent on the process.

Pressure
Volume
Temperature
Heat
4

A gas undergoes an adiabatic expansion from \( 10 \, \text{L} \) to \( 40 \, \text{L} \), reducing its pressure from \( 8 \, \text{atm} \) to \( 1 \, \text{atm} \). What is the value of \( \gamma \)?

For adiabatic: \( P_1 V_1^\gamma = P_2 V_2^\gamma \).

\( 8 \times 10^\gamma = 1 \times 40^\gamma \).

\( 8 = \left(\frac{40}{10}\right)^\gamma \Rightarrow 8 = 4^\gamma \).

\( 4^\gamma = 2^3 \Rightarrow 2^{2\gamma} = 2^3 \Rightarrow 2\gamma = 3 \Rightarrow \gamma = 1.5 \).

1.33
1.5
1.67
2.0
2

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