# An ideal gas is taken through the cycle $\;A \to B \to C \to A \;$ as shown in the figure . If the net heat supplied to the gas in the cycle is 5 J , the work done by the gas is the process $\;C \to A\;$ is

$(a)\;-5\;J\qquad(b)\;-10\;J\qquad(c)\;-15\;J\qquad(d)\;-20\;J$

Answer : $\;-5\;J$
Explanation :
In the cyclic process : $\; \bigtriangleup =0$
$\bigtriangleup Q = \bigtriangleup W$
$\bigtriangleup W = W_{A \to B} + W_{B \to C} + W_{C \to A}$
$W_{B \to C} =0 \;$ (Volume remains constant)
$W_{A \to B} = P (V_{2} -V_{1})\;$ (Pressure remains constant)
$= 10(2-1) = 10\;J$
Therefore , $5 = 10 + W_{C \to A}$
$W_{C \to A} = - 5 \;J$