Question

Two moles of nitrogen gas is kept in a cylinder of cross-section area $10c{m}^2$. The cylinder is closed by a light frictionless piston. Now the gas is slowly heated such that the displacement of the piston during the process is 50 cm, find the rise in temperature of the gas if 200 J of heat was added to the gas. (Atmospheric pressure $=100kPa,R=25/3J/mol-K)$

Answer 1

The change in internal energy of the gas is
$\Delta U=5/2nR\left(\Delta T\right)$
$=5/2\times 2R\times \left(\Delta T\right)=5R\times \Delta T$
The heat given to the gas $=200J$
The work done by the gas is
$W=\Delta Q-\Delta U$
$=200J-5R\Delta T$......(i)
As the distance moved by the piston is 50 cm, $\therefore$ the work done is
$\Delta W=P\Delta V=PA\Delta x={10}^5\times 10\times {10}^{-4}\times 50\times {10}^{-2}$ ......(ii)
From (i) and (ii)
$\Delta T=18/5K=3.6K$