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

Explanation

The change in internal energy of the gas is
`DeltaU = 5//2 nRT (DeltaT)`
`=5//2 xx 2R xx (DeltaT) = 5R xx DeltaT`
The heat given to the gas `= 200J`
The work done by the gas is
`W = DeltaQ - DeltaU`
`=200J - 5R DeltaT` ………..(i)
As the distance moved by the piston is `50cm,:.` the work done is
`DeltaW = PDeltaV = PA Deltax = 10^(5) xx 10 xx 10^(-4) xx 50 xx 10^(-2)` ........(ii)
From (i) and (ii)
`DeltaT = 18//5K = 3.6 K`