Thermodynamics Chapter-Wise Test 1

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A monatomic gas undergoes an adiabatic expansion from \( 700 \, \text{K} \) to \( 350 \, \text{K} \) with \( 2 \, \text{moles} \). What is the work done? (\( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \), \( \gamma = 1.67 \))

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

\( \mu = 2 \), \( R = 8.3 \), \( T_1 = 700 \), \( T_2 = 350 \), \( \gamma = 1.67 \).

\( W = \frac{2 \times 8.3 \times (700 - 350)}{1.67 - 1} = \frac{16.6 \times 350}{0.67} \approx 8671.6 \, \text{J} \approx 8672 \, \text{J} \).

8000 J
8672 J
9000 J
9500 J
2

Which of the following statements is incorrect regarding the Second Law of Thermodynamics?

The Second Law limits efficiency and directionality (e.g., no 100% heat-to-work conversion, Kelvin-Planck). Option B is incorrect; it contradicts the law, which requires heat rejection to a cold reservoir.

It restricts efficiency of heat engines
All heat can be converted to work in a single reservoir
Heat cannot flow from cold to hot without work
It governs natural process direction
2

How much heat is required to vaporize \( 0.9 \, \text{g} \) of water at \( 100^\circ \text{C} \) and \( 1 \, \text{atm} \)? (Latent heat = \( 2256 \, \text{J/g} \))

\( \Delta Q = m L \).

\( m = 0.9 \), \( L = 2256 \).

\( \Delta Q = 0.9 \times 2256 = 2030.4 \, \text{J} \approx 2030 \, \text{J} \).

1900 J
2030 J
2100 J
2200 J
2

A gas expands adiabatically from \( 9 \, \text{atm} \) and \( 18 \, \text{L} \) to \( 3 \, \text{atm} \). What is the final volume? (\( \gamma = 1.4 \))

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

\( 9 \times 18^{1.4} = 3 \times V_2^{1.4} \).

\( V_2^{1.4} = \frac{9}{3} \times 18^{1.4} = 3 \times 18^{1.4} \).

\( 18^{1.4} \approx 39.4 \), \( V_2^{1.4} = 3 \times 39.4 \approx 118.2 \).

\( V_2 = (118.2)^{1/1.4} \approx 31.8 \, \text{L} \).

28 L
31.8 L
34 L
36 L
2

Which of the following statements is correct regarding the Zeroth Law of Thermodynamics?

The Zeroth Law states that if two systems are in thermal equilibrium with a third, they are in equilibrium with each other, establishing temperature as a measurable property. It does not involve heat flow direction or work, which are addressed by other laws.

It dictates the direction of heat flow
It defines thermal equilibrium as a basis for temperature
It states that work equals heat supplied
It applies only to irreversible processes
2

A system in a cyclic process absorbs \( 940 \, \text{J} \) of heat and rejects \( 360 \, \text{J} \). What is the net work done?

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

\( Q_{\text{net}} = Q_{\text{absorb}} - Q_{\text{reject}} = 940 - 360 = 580 \, \text{J} \).

\( W = 580 \, \text{J} \).

500 J
580 J
620 J
700 J
2

A gas expands adiabatically, doing 360 J of work. What is the change in its internal energy?

Adiabatic: \( \Delta Q = 0 \), \( \Delta U = -\Delta W \). Work by gas: \( \Delta W = 360 \, \text{J} \). \( \Delta U = -360 \, \text{J} \).

-400 J
-360 J
-320 J
-300 J
2

In an isobaric process, \( 1.2 \, \text{moles} \) of gas expand from \( 350 \, \text{K} \) to \( 420 \, \text{K} \). What is the heat supplied if \( C_p = 25.5 \, \text{J mol}^{-1} \text{K}^{-1} \)?

\( \Delta Q = \mu C_p \Delta T \).

\( \mu = 1.2 \), \( C_p = 25.5 \), \( \Delta T = 420 - 350 = 70 \).

\( \Delta Q = 1.2 \times 25.5 \times 70 = 2142 \, \text{J} \).

2000 J
2142 J
2300 J
2500 J
2

A solid of \( 2 \, \text{moles} \) is heated from \( 300 \, \text{K} \) to \( 320 \, \text{K} \). If its molar specific heat capacity is \( 25.5 \, \text{J mol}^{-1} \text{K}^{-1} \), what is the heat supplied?

\( \Delta Q = \mu C \Delta T \).

\( \mu = 2 \), \( C = 25.5 \), \( \Delta T = 320 - 300 = 20 \).

\( \Delta Q = 2 \times 25.5 \times 20 = 1020 \, \text{J} \).

900 J
1020 J
1100 J
1200 J
2

What distinguishes work from heat as a mode of energy transfer?

Work involves energy transfer via macroscopic mechanical means (e.g., piston movement), not requiring a temperature difference, while heat is energy transferred due to a temperature gradient between the system and surroundings.

Work requires temperature difference
Heat involves mechanical motion
Work is mechanical, heat is thermal
Both are state variables
3

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