Thermodynamics Chapter-Wise Test 6

Correct answer Carries: 4.

Wrong Answer Carries: -1.

How many joules are equivalent to \( 300 \, \text{cal} \) of heat? (1 cal = \( 4.186 \, \text{J} \))

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

\( 300 \times 4.186 = 1255.8 \, \text{J} \approx 1256 \, \text{J} \).

1200 J
1256 J
1300 J
1350 J
2

A gas undergoes an isothermal expansion at \( 300 \, \text{K} \) from a volume of \( 2 \, \text{L} \) to \( 6 \, \text{L} \). If the number of moles of the gas is \( 0.1 \), what is the work done by the gas? (Take \( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \))

For an isothermal process, \( W = \mu R T \ln\left(\frac{V_2}{V_1}\right) \).

Substitute: \( \mu = 0.1 \), \( R = 8.3 \), \( T = 300 \), \( V_2 = 6 \), \( V_1 = 2 \).

\( W = 0.1 \times 8.3 \times 300 \times \ln\left(\frac{6}{2}\right) = 249 \times \ln(3) \).

\( \ln(3) \approx 1.0986 \), so \( W \approx 249 \times 1.0986 \approx 273.55 \, \text{J} \).

Rounded: \( W \approx 274 \, \text{J} \).

250 J
274 J
300 J
320 J
2

Which of the following statements is correct about the Second Law of Thermodynamics?

The Second Law states that some processes allowed by the First Law (e.g., heat-to-work conversion) are not feasible naturally, imposing directionality and irreversibility. Option B is correct.

All processes are reversible
It restricts some energy conversions
Heat equals work in all cases
Temperature remains constant
2

How much heat is required to raise the temperature of \( 0.3 \, \text{kg} \) of silver from \( 35^\circ \text{C} \) to \( 65^\circ \text{C} \)? (Specific heat of silver = \( 236.1 \, \text{J kg}^{-1} \text{K}^{-1} \))

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

\( m = 0.3 \), \( s = 236.1 \), \( \Delta T = 65 - 35 = 30 \).

\( \Delta Q = 0.3 \times 236.1 \times 30 = 2124.9 \, \text{J} \approx 2125 \, \text{J} \).

2000 J
2125 J
2200 J
2300 J
2

0.2 moles of an ideal gas expand isothermally at 350 K from 4 L to 10 L. What is the heat absorbed? (\( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \))

Isothermal: \( \Delta U = 0 \), \( \Delta Q = \Delta W = \mu R T \ln\left(\frac{V_2}{V_1}\right) \). \( \mu = 0.2 \), \( T = 350 \), \( V_2 = 10 \), \( V_1 = 4 \). \( \Delta Q = 0.2 \times 8.3 \times 350 \times \ln\left(\frac{10}{4}\right) = 581 \times 0.916 \approx 532 \, \text{J} \).

500 J
532 J
550 J
600 J
2

How much heat is required to raise the temperature of \( 0.25 \, \text{kg} \) of tungsten from \( 25^\circ \text{C} \) to \( 55^\circ \text{C} \)? (Specific heat of tungsten = \( 134.4 \, \text{J kg}^{-1} \text{K}^{-1} \))

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

\( m = 0.25 \), \( s = 134.4 \), \( \Delta T = 55 - 25 = 30 \).

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

900 J
1008 J
1100 J
1200 J
2

A system absorbs \( 690 \, \text{J} \) of heat and has \( 210 \, \text{J} \) of work done on it. What is the change in internal energy?

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

\( \Delta Q = 690 \), \( \Delta W = -210 \) (work on system).

\( 690 = \Delta U - 210 \Rightarrow \Delta U = 690 + 210 = 900 \, \text{J} \).

800 J
900 J
950 J
1000 J
2

An ideal gas expands isothermally at \( 380 \, \text{K} \) from \( 5 \, \text{L} \) to \( 15 \, \text{L} \) with \( 0.25 \, \text{moles} \). What is the work done by the gas? (\( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} \))

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

\( \mu = 0.25 \), \( R = 8.3 \), \( T = 380 \), \( V_2 = 15 \), \( V_1 = 5 \).

\( W = 0.25 \times 8.3 \times 380 \times \ln\left(\frac{15}{5}\right) = 788.5 \times \ln(3) \).

\( \ln(3) \approx 1.0986 \), \( W \approx 788.5 \times 1.0986 \approx 866 \, \text{J} \).

800 J
866 J
900 J
950 J
2

How many calories are equivalent to \( 836 \, \text{J} \) of heat? (1 cal = \( 4.186 \, \text{J} \))

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

\( \frac{836}{4.186} \approx 199.71 \approx 200 \, \text{cal} \).

180 cal
200 cal
220 cal
240 cal
2

How much heat is required to vaporize \( 0.7 \, \text{g} \) of water at \( 100^\circ \text{C} \) and \( 1 \, \text{atm} \)? (Latent heat = \( 2256 \, \text{J/g} \))

\( \Delta Q = m L \).

\( m = 0.7 \), \( L = 2256 \).

\( \Delta Q = 0.7 \times 2256 = 1579.2 \, \text{J} \approx 1579 \, \text{J} \).

1400 J
1579 J
1700 J
1800 J
2

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