Thermodynamics Chapter-Wise Test 16

Correct answer Carries: 4.

Wrong Answer Carries: -1.

What is the physical significance of the equation of state in thermodynamics?

The equation of state (e.g., \( P V = \mu R T \) for an ideal gas) relates state variables (pressure, volume, temperature), defining the equilibrium state of a system and showing their interdependence.

It measures heat transfer
It relates state variables
It calculates work done
It defines irreversibility
2

A gas expands adiabatically from \( 2 \, \text{atm} \) and \( 4 \, \text{L} \) to \( 1 \, \text{atm} \). What is the final volume? (\( \gamma = 1.33 \))

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

\( 2 \times 4^{1.33} = 1 \times V_2^{1.33} \).

\( V_2^{1.33} = 2 \times 4^{1.33} \).

\( V_2 = (2 \times 4^{1.33})^{1/1.33} = 2^{1/1.33} \times 4 \).

\( 2^{0.7519} \approx 1.681 \), \( V_2 \approx 1.681 \times 4 \approx 6.724 \, \text{L} \approx 6.7 \, \text{L} \).

5.5 L
6.7 L
7.5 L
8.0 L
2

How many calories are equivalent to \( 4186 \, \text{J} \) of heat? (1 cal = \( 4.186 \, \text{J} \))

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

\( \frac{4186}{4.186} = 1000 \, \text{cal} \).

500 cal
750 cal
1000 cal
1250 cal
3

What is the change in internal energy for \( 0.6 \, \text{moles} \) of an ideal gas heated from \( 270 \, \text{K} \) to \( 320 \, \text{K} \) at constant volume? (\( C_v = 20.8 \, \text{J mol}^{-1} \text{K}^{-1} \))

\( \Delta U = \mu C_v \Delta T \).

\( \mu = 0.6 \), \( C_v = 20.8 \), \( \Delta T = 320 - 270 = 50 \).

\( \Delta U = 0.6 \times 20.8 \times 50 = 624 \, \text{J} \).

580 J
624 J
650 J
700 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: \( C_v = \frac{5}{2} R \).

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

12.45 J mol⁻¹ K⁻¹
16.6 J mol⁻¹ K⁻¹
20.75 J mol⁻¹ K⁻¹
25.0 J mol⁻¹ K⁻¹
3

A system releases \( 870 \, \text{J} \) of heat and performs \( 330 \, \text{J} \) of work. What is the change in internal energy?

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

\( \Delta Q = -870 \) (heat released), \( \Delta W = 330 \) (work by system).

\( -870 = \Delta U + 330 \Rightarrow \Delta U = -870 - 330 = -1200 \, \text{J} \).

-1300 J
-1200 J
-1100 J
-1000 J
2

What is the primary reason a real gas deviates from the ideal gas equation?

Real gases deviate from the ideal gas equation (\( P V = \mu R T \)) due to intermolecular forces, which are negligible in ideal gases but significant in real gases, especially at high pressures or low temperatures.

Constant temperature
Intermolecular forces
Lack of pressure
No volume change
2

A gas expands adiabatically from \( 10 \, \text{atm} \) and \( 5 \, \text{L} \) to \( 2 \, \text{atm} \). What is the final volume? (\( \gamma = 1.33 \))

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

\( 10 \times 5^{1.33} = 2 \times V_2^{1.33} \).

\( V_2^{1.33} = \frac{10}{2} \times 5^{1.33} = 5 \times 5^{1.33} \).

\( 5^{1.33} \approx 9.62 \), \( V_2^{1.33} = 5 \times 9.62 \approx 48.1 \).

\( V_2 = (48.1)^{1/1.33} \approx 14.5 \, \text{L} \).

12 L
14.5 L
16 L
18 L
2

A system releases \( 760 \, \text{J} \) of heat and performs \( 240 \, \text{J} \) of work. What is the change in internal energy?

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

\( \Delta Q = -760 \) (heat released), \( \Delta W = 240 \) (work by system).

\( -760 = \Delta U + 240 \Rightarrow \Delta U = -760 - 240 = -1000 \, \text{J} \).

-1100 J
-1000 J
-900 J
-800 J
2

0.15 moles of an ideal gas at 320 K expand isothermally from 3 L to 9 L. What is the work done by the gas? (\( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \))

Isothermal: \( W = \mu R T \ln\left(\frac{V_2}{V_1}\right) \). \( \mu = 0.15 \), \( T = 320 \), \( V_2 = 9 \), \( V_1 = 3 \). \( W = 0.15 \times 8.3 \times 320 \times \ln\left(\frac{9}{3}\right) = 398.4 \times 1.0986 \approx 438 \, \text{J} \).

400 J
438 J
450 J
480 J
2

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