Which of the following shows the correct relationship between the pressure ‘P’ and density $$\rho $$ of an ideal gas at constant temperature ?

A Carnot freezer takes heat from water at 0^oC inside it and rejects it to the room at a temperature of 27^oC. The latent heat of ice is 336×10³ J kg⁻¹. If 5 kg of water at 0^oC is converted into ice at 0^oC by the freezer, then the energy consumed by the freezer is close to :

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) :