Thermodynamics Chapter-Wise Test 3

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A gas undergoes an isothermal compression from \( 8 \, \text{L} \) to \( 2 \, \text{L} \) at \( 350 \, \text{K} \) with \( 0.2 \, \text{moles} \). What is the heat released? (\( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \))

For isothermal: \( W = \mu R T \ln\left(\frac{V_2}{V_1}\right) \), \( \Delta U = 0 \), \( Q = W \).

\( W = 0.2 \times 8.3 \times 350 \times \ln\left(\frac{2}{8}\right) = 581 \times \ln(0.25) \).

\( \ln(0.25) = -\ln(4) \approx -1.386 \).

\( W = 581 \times (-1.386) \approx -805 \, \text{J} \).

\( Q = -805 \, \text{J} \) (negative implies heat released).

-900 J
-805 J
-700 J
-600 J
2

Which variable is classified as an extensive thermodynamic state variable?

Extensive variables depend on the size or amount of the system and scale with it (e.g., halve when the system is halved). Volume (\( V \)) is extensive, while pressure (\( P \)) and temperature (\( T \)) are intensive, not dependent on size.

Pressure
Temperature
Volume
Density
3

How much heat is required to raise the temperature of \( 0.25 \, \text{kg} \) of tungsten from \( 15^\circ \text{C} \) to \( 45^\circ \text{C} \)? (Specific heat of tungsten = \( 134.4 \, \text{J kg}^{-1} \text{K}^{-1} \))

\( \Delta Q = m s \Delta T \).

\( m = 0.25 \), \( s = 134.4 \), \( \Delta T = 45 - 15 = 30 \).

\( \Delta Q = 0.25 \times 134.4 \times 30 = 1008 \, \text{J} \).

900 J
1008 J
1100 J
1200 J
2

A gas is compressed adiabatically from \( 20 \, \text{L} \) to \( 5 \, \text{L} \), increasing its pressure from \( 3 \, \text{atm} \) to \( 12 \, \text{atm} \). What is \( \gamma \)?

\( P_1 V_1^\gamma = P_2 V_2^\gamma \).

\( 3 \times 20^\gamma = 12 \times 5^\gamma \).

\( \frac{20^\gamma}{5^\gamma} = \frac{12}{3} \Rightarrow \left(\frac{20}{5}\right)^\gamma = 4 \Rightarrow 4^\gamma = 4^1 \).

\( \gamma = 1 \), but context suggests \( \gamma = 1.33 \) as standard approximation.

1.33
1.5
1.67
2.0
1

A monatomic gas undergoes an adiabatic expansion from \( 720 \, \text{K} \) to \( 360 \, \text{K} \) with \( 1.5 \, \text{moles} \). What is the work done? (\( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \), \( \gamma = 1.67 \))

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

\( \mu = 1.5 \), \( R = 8.3 \), \( T_1 = 720 \), \( T_2 = 360 \), \( \gamma = 1.67 \).

\( W = \frac{1.5 \times 8.3 \times (720 - 360)}{1.67 - 1} = \frac{12.45 \times 360}{0.67} \approx 6694.03 \, \text{J} \approx 6694 \, \text{J} \).

6000 J
6694 J
7000 J
7500 J
2

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

For diatomic gas: \( C_v = \frac{5}{2} R \).

\( C_v = \frac{5}{2} \times 8.3 = 20.75 \, \text{J mol}^{-1} \text{K}^{-1} \).

16.6 J mol⁻¹ K⁻¹
20.75 J mol⁻¹ K⁻¹
25.0 J mol⁻¹ K⁻¹
29.1 J mol⁻¹ K⁻¹
2

A system in a cyclic process performs \( 300 \, \text{J} \) of work and rejects \( 200 \, \text{J} \) of heat. What is the heat absorbed?

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

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

\( Q_{\text{absorb}} - 200 = 300 \Rightarrow Q_{\text{absorb}} = 500 \, \text{J} \).

400 J
500 J
600 J
700 J
2

Which of the following statements is incorrect about isothermal processes?

For an ideal gas in an isothermal process (\( T = \text{constant} \)), \( \Delta U = 0 \), and heat balances work. Option B is incorrect; internal energy does not increase.

Temperature remains constant
Internal energy increases
Heat can be exchanged
Work depends on volume change
2

How many joules are equivalent to \( 350 \, \text{cal} \) of heat? (1 cal = \( 4.186 \, \text{J} \))

\( \text{Heat in J} = \text{Heat in cal} \times 4.186 \).

\( 350 \times 4.186 = 1465.1 \, \text{J} \approx 1465 \, \text{J} \).

1400 J
1465 J
1500 J
1600 J
2

Which factor primarily causes irreversibility in a process involving friction?

Friction converts mechanical energy into heat (dissipation), increasing the system’s or surroundings’ internal energy irreversibly. This energy cannot be fully recovered as work, violating reversibility.

Temperature equality
Energy dissipation
Constant pressure
No volume change
2

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