Question

A student records $\Delta Q,\Delta U,\Delta W$ for a thermodynamic cycle $ABCA$. Certain entries are missing. Find correct entry in following options.

• A. $W_{BC}=-70J$
• B. $\Delta Q_{CA}=-130J$
• C. $\Delta U_{AB}=190J$
• D. $\Delta U_{CA}=-160J$

Answer 1

Answer: (B), (D)

$\Delta U_{CA}=-160J$
$\Delta Q_{CA}=-130J$

Using $\Delta Q=\Delta U+\Delta W$

For AB; $150=\Delta U_{AB}+40⟹\Delta U_{AB}=110J$

For BC; $10=\Delta W_{BC}+50⟹\Delta W_{BC}=-40J$

Also internal energy change over complete cycle must be zero.

Thus, $110+50+\Delta U_{CA}=0⟹\Delta U_{CA}=-160J$

$\Delta W_T=40+30-40=30J$

So, $\Delta Q_T=30J⟹150+10+\Delta Q_{CA}=30$

Thus, $\Delta Q_{CA}=-130J$