Ncert Exercises & Solutions

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)

(3) Hint: The internal energy is a path-dependent variable.

Step 1: Find the change in internal energy.

Change in internal energy for the process A to B,

{dU}_{A \to B} = {nC}_{v} dT = {nC}_{v} (T_{B} - T_{A})

which depends only on temperatures at A and B.

Step 2: Find the work done.

Work done for A to B,

{dW}_{A \to B} =

Area under the P-V curve which is maximum for the path I.

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