Question

An ideal gas is taken from state 1 to state 2 through optional path $A, B, C$ and $D$ as shown in the $P V$ diagram. Let $Q, W$ and $U$ represent the heat supplied, work done and change in internal energy of the gas respectively. Then,

• A. $Q_{A}-Q_{D}=W_{A}-W_{D}$
• B. $Q_{B}-W_{B} > Q_{C}-W_{C}$
• C. $W_{A} < W_{B} < W_{C} < W_{D}$
• D. $Q_{A} < Q_{B} < Q_{C} < Q_{D}$

Answer 1

Answer: (A)

Work done by gas in all four process is positive and in order
$W_{A} > W_{B} > W_{C} > W_{D}$
$\Rightarrow $ (c) is false
The change in initial energy $U$ is same for all process.
$\therefore Q_{A}=U +W_{A}$ ...(1)
$Q_{B}=U+W_{B}$ ...(2)
$Q_{C}=U+W_{C}$ ...(3)
$Q_{D}=U+W_{D}$ ...(4)
Hence $Q_{A} > Q_{B} > Q_{C} > Q_{D}$
$\Rightarrow $ (d) is false
from equations (1) and (4)
$Q_{A}-Q_{D}=W_{A}-W_{D}$
$\Rightarrow $ (a) is true
from equations (2) and (3)
$Q_{B}-Q_{C}=W_{B}-W_{C}$
$\Rightarrow $ (b) is false.