Question
A thermodynamic system is taken through the cycle $$ABCD$$ as shown in figure. Heat rejected by the gas during the cycle is
A thermodynamic system is taken through the cycle $$ABCD$$ as shown in figure. Heat rejected by the gas during the cycle is
A.
$$2\,pV$$
B.
$$4\,pV$$
C.
$$\frac{1}{2}pV$$
D.
$$pV$$
Answer :
$$2\,pV$$
Solution :
For given cyclic process, $$\Delta U = 0 \Rightarrow Q = W$$
Also, $$W = - $$ area enclosed by the curve
$$\eqalign{ & = - AB \times AD \cr & = - \left( {2p - p} \right)\left( {3V - V} \right) \cr & = - p \times 2V \cr} $$
∴ Heat rejected $$ = 2\,pV$$
For given cyclic process, $$\Delta U = 0 \Rightarrow Q = W$$
Also, $$W = - $$ area enclosed by the curve
$$\eqalign{ & = - AB \times AD \cr & = - \left( {2p - p} \right)\left( {3V - V} \right) \cr & = - p \times 2V \cr} $$
∴ Heat rejected $$ = 2\,pV$$
