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Q.
A diatomic .gas $(\gamma=1.4)$ does $2000\, J$ of work when it is expanded isobarically. Find the heat (in $kJ$ ) given to the gas in the above process.
Thermodynamics
Solution:
For a diatomic gas, $C_{v}=\frac{5}{2} R$
and $C_{p}=\frac{7}{2} R$.
The work done in an isobaric process is
$W=P\left(V_{2}-V_{1}\right)=n R T_{2}-n R T_{1}$
$ \Rightarrow T_{2}-T_{1}=\frac{W}{n R}$
The heat given in an isobaric process is .
$Q =n C_{p}\left(T_{2}-T_{1}\right)=n C_{p} \frac{W}{n R}=\frac{7}{2} \times W $
$=\frac{7}{2} \times 2000\, J =7000 \,J$