A gas is enclosed in a cylindrical vessel fitted with a frictionl… - Vidyadip

Question

A gas is enclosed in a cylindrical vessel fitted with a frictionless piston. The gas is slowly heated for some time. During the process, $10\ J$ of heat is supplied and the piston is found to move out $10\ cm$ . Find the increase in the internal energy of the gas. The area of cross section of the cylinder $=4 \mathrm{~cm}^2$ and the atmospheric pressure $=100 \mathrm{kPa}$.

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Answer

$d Q=10 J$
$d V=A \times 10 \mathrm{~cm}^3=4 \times 10 \mathrm{~cm}^3=40 \times 10^{-6} \mathrm{~cm}^3$
$d w=P d v=100 \times 10^3 \times 40 \times 10^{-6}=4 \mathrm{~cm}^3$
$d u=?$
$10=\mathrm{du}+\mathrm{dw}$
$\Rightarrow 10=\mathrm{du}+4$
$\Rightarrow \mathrm{du}=6 \mathrm{~J}$

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