Question

Isothermal Process.

Answer 1

Isothermal Process

For such a process temperature remains constant throughout the process. Hence $P V=$ constant as $T$ is constant. Work is done at the same rate as heat is supplied, hence there is no increase of internal energy.

Due to this, $\Delta U=0$ and thus $\Delta Q=\Delta W$.

Work done during an isothermal process,

$W=\mu R T \ln \left(\frac{V_{2}}{V_{1}}\right)=\mu R T \ln \left(\frac{P_{1}}{P_{2}}\right)$

The slope of isothermal curve on a $P-V$ diagram at any point on the curve is given by

$\frac{d P}{d V}=\frac{-P}{V}$

Note : In an isothermal expansion the gas absorbs heat and does work and in an isothermal compression work is done on the gas by the environment and heat is released.