Q. No.A Carnot engine whose sink is at \(300~\text{K}\) has an efficiency of \(40\%.\) By how much should the temperature of the source be increased to increase its efficiency by \(50\%\) of its original efficiency?
1.
\(275~\text{K}\)
2.
\(325~\text{K}\)
3.
\(250~\text{K}\)
4.
\(380~\text{K}\)
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One mole of an ideal gas expands at a constant temperature of \(300~\text{K}\) from an initial volume of \(10\) litres to a final volume of \(20\) litres.
The work done in expanding the gas is equal to:
(\(R = 8.31\) J/mole-K)
1. \(750~\text{J}\)
2. \(1728~\text{J}\)
3. \(1500~\text{J}\)
4. \(3456~\text{J}\)
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The pressure of a monoatomic gas increases linearly from \(4\times 10^5~\text{N/m}^2\) to \(8\times 10^5~\text{N/m}^2\) when its volume increases from \(0.2 ~\text m^3\) to \(0.5 ~\text m^3.\) The work done by the gas is:
1. \(2 . 8 \times10^{5}~\text J\)
2. \(1 . 8 \times10^{6}~\text J\)
3. \(1 . 8 \times10^{5}~\text J\)
4. \(1 . 8 \times10^{2}~\text J\)
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| 1. | \(1000~\text{J}\) | 2. | zero |
| 3. | \(-2000~\text{J}\) | 4. | \(2000~\text{J}\) |
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A thermodynamic system undergoes a cyclic process \(ABCDA\) as shown in Fig. The work done by the system in the cycle is:
| 1. | \( P_0 V_0 \) | 2. | \( 2 P_0 V_0 \) |
| 3. | \(\dfrac{P_0 V_0}{2} \) | 4. | zero |
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| 1. | \(64P\) | 2. | \(32P\) |
| 3. | \(\frac{P}{64}\) | 4. | \(16P\) |
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(Take, 1 cal= 4.2 Joules)
1. 23.65 W
2. 236.5 W
3. 2365 W
4. 2.365 W
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A horizontal cylinder has two sections of unequal cross-sections in which two pistons, A and B, can move freely. The pistons are joined by a string. Some gas is trapped between the pistons. If this gas is heated, the pistons will:
| 1. | move to the left. |
| 2. | move to the right. |
| 3. | remain stationary. |
| 4. | move either to the left or to the right depending on the initial pressure of the gas. |
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In the \((P\text-V)\) diagram shown, the gas does \(5~\text J\) of work in the isothermal process \(ab\) and \(4~\text J\) in the adiabatic process \(bc.\) What will be the change in internal energy of the gas in the straight path from \(c\) to \(a?\)
1. \(9~\text J\)
2. \(1~\text J\)
3. \(4~\text J\)
4. \(5~\text J\)
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