1 mole of rigid diatomic gas performs a work of $${Q \over 5}$$ when heat Q is supplied to it. The molar heat capacity of the gas during this transformation is $${xR \over 8}$$. The value of x is _________. [R = universal gas constant]

The volume V of a given mass of monoatomic gas changes with temperature T according to the relation $$V = K{T^{{2 \over 3}}}$$. The workdone when temperature changes by 90K will be xR. The value of x is _________. [R = universal gas constant]

A container is divided into two chambers by a partition. The volume of first chamber is 4.5 litre and second chamber is 5.5 litre. The first chamber contain 3.0 moles of gas at pressure 2.0 atm and second chamber contain 4.0 moles of gas at pressure 3.0 atm. After the partition is removed and the mixture attains equilibrium, then, the common equilibrium pressure existing in the mixture is x $$\times$$ 10^$$-$$1 atm. Value of x is ________.

A reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced by 52K, its efficiency is doubled. The temperature in Kelvin of the source will be __________.