# A diamotic gas is heated at constant pressure such that it performs 4 J of work . Find the heat supplied to the gas

$(a)\;15\;J\qquad(b)\;11\;J\qquad(c)\;10\;J\qquad(d)\;14\;J$

Answer : $\;14\;J$
Explanation :
Work done at constant pressure
$=P \bigtriangleup V=P\;(V_{2}-V_{1}) = 4 J$
$PV=nRT$
$PV_{1}=nRT_{1}----(1)$
$P(V_{2}-V_{1})=nR(T_{2}-T_{1})=4$
$PV_{2}nRT_{2}-----(2)$
$\bigtriangleup u= \large\frac{nR}{(r-1)}\;(T_{2}-T_{1})=\large\frac{4}{r-1}$
For a diamatic gas , $\;r=\large\frac{7}{5}$
Therefore , $\;\bigtriangleup u =\large\frac{4}{\large\frac{7}{5}-1}=5 \times 2=10 J$
$\bigtriangleup Q = \bigtriangleup u + \bigtriangleup w$
$=10+4 = 14 J$