Question

An ideal gas undergoes a series of processes represented by $A\to B\to C\to D$ on the P-V diagram. Then,

• A. Internal energy of gas at B and D are equal
• B. The work done by gas in $A\to B\to C\to D$ is $\frac{-3}{2}{P}_o{V}_o$
• C. Points B and D lie on an isotherm.
• D. Ratio of internal energy of the gas in state A to that in state D is 4.

Answer 1

Answer: (A), (B), (C)

The correct options are
A Internal energy of gas at B and D are equal
B The work done by gas in $A\to B\to C\to D$ is $\frac{-3}{2}{P}_o{V}_o$
C Points B and D lie on an isotherm.

(a) Product PV is same at B and D. Temperature is same at these points.
(b) $W=\frac{3}{2}{P}_o\frac{V_o}{3}-\left(2P_o\right)V_o=-\frac{3}{2}{P}_o{V}_o$
(c) Yes
(d) Internal energy is proportional to temperature, which is proportional to product of pressure and volume. Hence the answer is 2.