A given sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T. The mass of each molecule of the gas is m. Which of the following gives the density of the gas ?

A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then

The molecules of a given mass of a gas have r.m.s. velocity of 2000 m s^$$-$$1 at 27^oC and 1.0 $$ \times $$ 10⁵ N m^$$-$$2 pressure. When the temperature and pressure of the gas are respectively, 127^oC and 0.05 $$ \times $$ 10⁵ N m^$$-$$2, the r.m.s. velocity of its molecules in m s^$$-$$1 is

A refrigerator works between 4^oC and 30^oC. It is required to remove 600 calories of heat every second in order to keep the temperature of the refrigerated space constant. The power required is (Take 1 cal = 4.2 Joules)