A thermally insulated vessel contains 150g of water at 0°C. Then the air from the vessel is pumped out adiabatically. A fraction of water turns into ice and the rest evaporates at 0°C itself. The mass of evaporated water will be closest to : (Latent heat of vaporization of water = 2.10 × 10⁶ J kg^–1 and Latent heat of Fusion of water = 3.36 × 10⁵ J kg^–1)

A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is $$\ell $$₁, and that below the piston is $$\ell $$₂, such that $$\ell $$₁ > $$\ell $$₂. Each part of the cylinder contains n moles of an ideal gas at equal temperature T. If the piston is stationary, its mass, m, will be given by :
(R is universal gas constant and g is the acceleration due to gravity)

An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature 300 K. The mean time between two successive collisions is 6 $$ \times $$ 10^–8 s. If the pressure is doubled and temperature is increased to 500 K, the mean time between two successive collisions will be close to

For the given cyclic process CAB as shown for a gas, the work done is :