A closed system undergoes a process $$1 \to 2$$ for which the values $${W_{1 - 2}}$$ and $${Q_{1 - 2}}$$ are $$50\,kJ$$ and $$- 20\,kJ$$ respectively. If the system is returned to state 1 and $${Q_{2 \to 1}}$$ is $$+ 10\,kJ$$ the work done $${W_{2 \to 1}}$$ is
A.
$$40\,kJ$$
B.
$$50\,kJ$$
C.
$$-60\,kJ$$
D.
$$-50\,kJ$$
Answer :
$$-60\,kJ$$
Solution :
$$\eqalign{
& - 20 = \Delta U + 50 \Rightarrow \Delta U = - 70. \cr
& {\text{From}}\,\,2 \to 1,\,\Delta U = 70\,kJ. \cr
& {\text{Now}}\,\,10 = 70 + W \Rightarrow W = - 60\,kJ. \cr} $$
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