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)

Two identical beakers A and B contain equal volumes of two different liquids at 60°C each and left to cool down. Liquid in A has density of 8 × 10² kg/m³ and specific heat of 2000 J kg^–1 K^–1 while liquid in B has density of 10³ kg m^–3 and specific heat of 4000 J kg^–1 K^–1. Which of the following best describes their temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same)

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