Assertion (A): | If the efficiency of the engine is \(\frac1n,\) then the coefficient of performance of the reversed cycle working as a refrigerator is \(n-1\). |
Reason (R): | \(1-\frac{T_{\text{low}}}{T_{\text{high}}},\) while the coefficient of performance of the reversed cycle is \(\frac{T_{\text{low}}}{T_{\text{high}~-~T_{\text{low}}}}\). | The efficiency of Carnot's cycle is
1. | (A) is true but (R) is false. |
2. | (A) is false but (R) is true. |
3. | Both (A) and (R) are true and (R) is the correct explanation of (A). |
4. | Both (A) and (R) are true but (R) is not the correct explanation of (A). |
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. |
1. | only (I) is correct |
2. | only (II) is correct |
3. | both (I) and (II) are correct |
4. | none of them are correct |
Consider the following two statements.
(A): | If heat is added to a system, its temperature must increase. |
(B): | If positive work is done by a system in a thermodynamic process, its volume must increase. |
1. | Both A and B are correct. |
2. | A is correct but B is wrong. |
3. | B is correct but A is wrong. |
4. | Both A and B are wrong. |
The figure shows the (P-V) diagram of an ideal gas undergoing a change of state from A to B. Four different paths I, II, III and 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 IV and III but not in cases I and II. |
b. | The change in internal energy is the same in all four cases. |
c. | Work done is maximum in case I. |
d. | Work done is minimum in case II. |
Which of the following options contains only correct statements?
1. | (b), (c), (d) | 2. | (a), (d) |
3. | (b), (c) | 4. | (a), (c), (d) |
Assertion (A): | It is not possible for a system, unaided by an external agency to transfer heat from a body at a lower temperature to another at a higher temperature. |
Reason (R): | It is not possible to violate the second law of thermodynamics. |
1. | Both (A) and (R) are true and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are true but (R) is not the correct explanation of (A). |
3. | (A) is true but (R) is false. |
4. | Both (A) and (R) are false. |
Statement (A): | Heat is not a state function. |
Statement (B): | Heat supplied to a system is a path function. |
1. | Both statements (A) and (B) are true. |
2. | Both statements (A) and (B) are false. |
3. | Only statement (A) is true. |
4. | Only statement (B) is true. |
A gas expands from \(\mathrm{i}\) to \(\mathrm{f}\) along the three paths indicated. The work done along the three paths denoted by have the relationship:
1.
2.
3.
4.
An ideal gas is made to undergo a cycle depicted by the \((P-V)\) 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, \(1-\frac{T_2}{T_1}.\) |
4. | the cycle can only be carried out in the reverse direction as shown in the figure. |
In this \((P-V)\) diagram below the dashed curved line is adiabatic.
For a process, that is described by a straight line joining two points \(X\) and \(Y\) on the adiabat (solid line In the diagram) heat is:
(Consider the variations in temperature from \(X\) to \(Y\) along the straight line.)
1. | \(X\) to \(Y.\) | absorbed throughout from
2. | \(X\) to \(Y.\) | released throughout from
3. | \(X\) up to an intermediate point \(Z\) (not shown In the figure) and then released from \(Z\) to \(Y.\) | absorbed from
4. | \(X\) up to an Intermediate point \(Z\) (not shown in the figure) and then absorbed from \(Z\) to \(Y.\) | released from
An ideal gas is taken reversibly around the cycle a-b-c-d-a as shown on the \(T\) (temperature) -\(S\) (entropy) diagram.
The most appropriate representation of the above cycle on a \(U\) (internal energy) -\(V\) (volume) diagram is:
1. | 2. | ||
3. | 4. |