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) Work done is maximum in case \(\mathrm{I}\).
(d) 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)

Subtopic:  Work Done by a Gas |
 78%
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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) \(\Delta U=0\)
 
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)
Subtopic:  Types of Processes |
 89%
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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.
Subtopic:  Work Done by a Gas |
 54%
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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

Subtopic:  Types of Processes |
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For ideal diatomic gases at normal temperature,
 
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
Subtopic:  Molar Specific Heat |
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A gas expands from \(i\) to \(f\) along the three paths indicated. The work done along the three paths denoted by \(W_1, W_2, ~\text{and}~W_3\) have the relationship:
                
1. \(W_1<W_2<W_3\)
2. \(W_2<W_1=W_3\)
3. \(W_2<W_1<W_3\)
4. \(W_1>W_2>W_3\)
Subtopic:  Work Done by a Gas |
 67%
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An ideal gas is taken reversibly around the cycle \(a\text-b\text-c\text-d\text-a\) as shown on the \(T\) (temperature) \(\text-S\) (entropy) diagram.
                  
The most appropriate representation of the above cycle on a \(U\) (internal energy) \(\text-V\) (volume) diagram is:

1. 2.
3. 4.
Subtopic:  Basic Terms |
 65%
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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. absorbed throughout from \(X\) to \(Y.\)
2. released throughout from \(X\) to \(Y.\)
3. absorbed from \(X\) up to an intermediate point \(Z\) (not shown In the figure) and then released from \(Z\) to \(Y.\)
4. released from \(X\) up to an Intermediate point \(Z\) (not shown in the figure) and then absorbed from \(Z\) to \(Y.\)
Subtopic:  Types of Processes |
 57%
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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.
Subtopic:  Cyclic Process |
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One mole of a diatomic ideal gas undergoes a cyclic process \(ABC\) as shown in the figure. The process \(BC\) is adiabatic. The temperatures at \(A,\) \(B,\) and \(C\) are \(400\) K, \(800\) K, and \(600\) K respectively. Choose the correct statement:
               
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 \(-350R.\)
Subtopic:  Cyclic Process |
 72%
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