Ncert Exercises & Solutions

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)

(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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