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. |
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.
Thermodynamic processes are indicated in the following diagram:
Match the following:
Column-I | Column-II | ||
P. | Process I | a. | Adiabatic |
Q. | Process II | b. | Isobaric |
R. | Process III | c. | Isochoric |
S. | Process IV | d. | Isothermal |
P | Q | R | S | |
1. | c | a | d | b |
2. | c | d | b | a |
3. | d | b | a | c |
4. | a | c | d | b |
The Carnot cycle (reversible) of gas is represented by a pressure-volume curve as shown. Consider the following statements:
I. | Area ABCD = Work done on the gas |
II. | Area ABCD = Net heat absorbed |
III. | Change in the internal energy in cycle = 0 |
Which of the statement(s) given above is/are correct?
1. | I only | 2. | II only |
3. | II and III | 4. | I, II and III |
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) |
Match the thermodynamic processes taking place in a system with the correct conditions. In the table, Q is the heat supplied, W is the work done and 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) | \(\Delta U=0\) |
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.
(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. |
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