Question

The figure represents a closed cycle for the gas. The change in internal energy of the gas as it moves from $a$ to $c$ along path $abc$ is $-200\text{J}$. As it moves from $c$ to $d$, $180\text{J}$ must be transferred to it as heat, An additional transfer of $80\text{J}$ to it as heat is needed, as it moves from $d$ to $a$. How much work is done on the gas as it moves from $c$ to $d$ ?

• A. $60\text{J}$
• B. $50\text{J}$
• C. $30\text{J}$
• D. $80\text{J}$

Answer 1

The correct option is A $60\text{J}$

Along process d $\to a$, work done = $0\text{J}$
$\Rightarrow Q_{da}=\Delta U_{da}=+80\text{J}$
and for cyclic process $abcda$, we can write that,
$\Delta U_{ac}+\Delta U_{cd}+\Delta U_{da}=0$
$\Rightarrow -200\text{J}+\Delta U_{cd}+80\text{J}=0$
$\Rightarrow \Delta U_{cd}=+120\text{J}$
Using first law of thermodynamics, we can say that
$W_{cd}=Q_{cd}-\Delta U_{cd}$
$W_{cd}=+180\text{J}-120\text{J}$
$W_{cd}=+60\text{J}$
Hence, option (a) is the correct answer.