Q. No.The figure shows the \((P\text-V)\) diagram of an ideal gas undergoing a change of state from \(A\) to \(B.\) Four different paths \(\mathrm{I, II, III}\) and \(\mathrm{IV},\) as shown in the figure, may lead to the same change of state.
| (a) | The change in internal energy is the same in cases \(\mathrm{IV}\) and \(\mathrm{III}\) but not in cases \(\mathrm{I}\) and \(\mathrm{II}.\) |
| (b) | The change in internal energy is the same in all four cases. |
| (c) | The work done is maximum in case \(\mathrm{I}.\) |
| (d) | The work done is minimum in case \(\mathrm{II}.\) |
Which of the following options contains only correct statements?
| 1. | (b), (c), (d) | 2. | (a), (d) |
| 3. | (b), (c) | 4. | (a), (c), (d) |
A given mass of gas expands from state \(A\) to state \(B\) by three paths \(1, 2~\text{and}~3\), as shown in the figure. If \(W_1, W_2~\text{and}~W_3\) respectively be the work done by the gas along the three paths, then:
| 1. | \(W_1 >W_2>W_3\) | 2. | \(W_1<W_2<W_3\) |
| 3. | \(W_1 =W_2=W_3\) | 4. | \(W_1 <W_2=W_3\) |
A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then:
| 1. | compressing the gas through an adiabatic process will require more work to be done. |
| 2. | compressing the gas isothermally or adiabatically will require the same amount of work to be done. |
| 3. | which of the case (whether compression through isothermal or through the adiabatic process) requires more work to be done will depend upon the atomicity of the gas. |
| 4. | compressing the gas isothermally will require more work to be done. |
The pressure-temperature \((P\text-T)\) graph for two processes, \(A\) and \(B,\) in a system is shown in the figure. If \(W_1\) and \(W_2\) are work done by the gas in process \(A\) and \(B\) respectively, then:
| 1. | \(W_{1}=W_2\) | 2. | \(W_{1}<W_2\) |
| 3. | \(W_{1}>W_2\) | 4. | \(W_{1}= - W_2\) |
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. \(3456~\text{J}\)
An ideal gas is compressed to half its initial volume by means of several processes.
Which of the following processes results in the maximum work being done on the gas?
1. Adiabatic
2. Isobaric
3. Isochoric
4. Isothermal
Two identical samples of a gas are allowed to expand, (i) isothermally and (ii) adiabatically. The work done will be:
| 1. | more in the isothermal process. |
| 2. | more in the adiabatic process. |
| 3. | equal in both processes. |
| 4. | none of the above. |
| 1. |  |
2. |  |
| 3. |  |
4. |  |
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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