A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2 s at T=0^oC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is $$\alpha $$ then the value of S is :

200 g water is heated from 40^oC to 60^oC. Ignoring the slight expansion of water, the change in its internal energy is close to (Given specific heat of water = 4184 J/kg/K) :

The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is :

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity $$C$$ remains constant. If during this process the relation of pressure $$P$$ and volume $$V$$ is given by $$P{V^n} = $$ constant, then $$n$$ is given by (Here $${C_p}$$ and $${C_v}$$ are molar specific heat at constant pressure and constant volume, respectively: