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) and (d) only
2.
(a) and (d) only
3.
(b) and (c) only
4.
(a), (c) and (d) only
Which of the following options contains only correct statements?
Match the thermodynamic processes taking place in a system with the correct conditions. In the table, \(\Delta Q\) is the heat supplied, \(\Delta W\) is the work done and \(\Delta U\) is the change in internal energy of the system.
| Process | Condition | ||
| (I) | Adiabatic | (A) | \(\Delta W=0\) |
| (II) | Isothermal | (B) | \(\Delta Q=0\) |
| (III) | Isochoric | (C) | \(\Delta U\neq0, \Delta W\neq0,\Delta Q\neq0\) |
| (IV) | Isobaric | (D) | \(\Delta U=0\) |
Codes:
| 1. | (I) – (B), (II) – (A), (III) – (D), (IV) – (C) |
| 2. | (I) – (A), (II) – (A), (III) – (B), (IV) – (C) |
| 3. | (I) – (A), (II) – (B), (III) – (D), (IV) – (D) |
| 4. | (I) – (B), (II) – (D), (III) – (A), (IV) – (C) |
Consider the following two statements.
| Statement I: | If heat is added to a system, its temperature must increase. |
| Statement II: | If positive work is done by a system in a thermodynamic process, its volume must increase. |
| 1. | Both Statement I and Statement II are correct. |
| 2. | Statement I is correct and Statement II is incorrect. |
| 3. | Statement I is incorrect and Statement II is correct. |
| 4. | Both Statement I and Statement II are incorrect. |
Figure shows P-T diagram for given mass of an ideal gas for the process A→B. During this process, density of the gas is
1. Decreasing
2. Increasing
3. Constant
4. First decreasing then increasing
| Statement I: | Molar heat capacity at constant pressure for all diatomic gases is the same. |
| Statement II: | The specific heat capacity at constant pressure of all diatomic ideal gases is the same. |
Choose the correct statement(s):
| 1. | only (I) is correct |
| 2. | only (II) is correct |
| 3. | both (I) and (II) are correct |
| 4. | none of them are correct |
| 1. | \(W_1<W_2<W_3\) | 2. | \(W_2<W_1=W_3\) |
| 3. | \(W_2<W_1<W_3\) | 4. | \(W_1>W_2>W_3\) |
An ideal gas is taken reversibly around the cycle \(a\text-b\text-c\text-d\text-a\) as shown on the temperature \((T)\) - entropy \((S)\) diagram.
The most appropriate representation of the above cycle on an internal energy \((U)\) - volume \((V)\) diagram is:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
An ideal gas is made to undergo a cycle depicted by the \((P\text-V)\) diagram alongside. If the curved line from \(A\) to \(B\) is adiabatic, then:
| 1. | The efficiency of this cycle is given by unity, as no heat is released during the cycle. |
| 2. | Heat is absorbed in the upper part of the straight-line path and released in the lower. |
| 3. | If \(T_1\) and \(T_2\) are the maximum and minimum temperatures reached during the cycle, then the efficiency is given by, \(\left(1-\dfrac{T_2}{T_1}\right).\) |
| 4. | The cycle can only be carried out in the reverse direction as shown in the figure. |
| 1. | The change in internal energy in the process \(BC\) is \(-500R.\) |
| 2. | The change in internal energy in the whole cyclic process is \(250R.\) |
| 3. | The change in internal energy in the process \(CA\) is \(700R.\) |
| 4. | The change in internal energy in the process \(AB\) is \(-350R.\) |
| 1. | The magnitude of the work done by the gas is \(RT_{0}\ln 2.\) |
| 2. | The work done by the gas is \(V_{0}T_{0}.\) |
| 3. | The net work done by the gas is zero. |
| 4. | The work done by the gas is \(2RT_{0}\ln2.\) |
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