Question

A gas is taken through a cyclic process. The change in internal energy along the path from c to a is –$160J$. Heat transferred along the path from a to $b$ is $200J$ and $40J$ for path $b$ to $c$. Then

• A. work done in the cycle is less than $80J$
• B. work done in path abc is $80J$
• C. work done in path ab is $160J$
• D. heat transferred in the system is less than $80J$

Answer 1

Answer: (A), (B), (D)

heat transferred in the system is less than $80J$

For cyclic process $Q_{net}=W_{net}$
Since $U_{cycle}=0$
$Q_{ab}+Q_{bc}+Q_{ca}=W_{ab}+W_{bc}+W_{ca}$
$200J+40J+Q_{ca}=W_{ab}+W_{bc}+W_{ca}$
$240J+Q_{ca}=W_{abc}+W_{ca}$
$240J+Q_{ca}-W_{ca}=W_{abc}$
$240-160=W_{abc}$
And, $W_{bc}=0$
$\Rightarrow \Delta U_{bc}=40$
$\Rightarrow W_{ab}=80$
Work done in path ca is negative, so options a and d are correct.