A heat engine operates with the cold reservoir at temperature 324 K. The minimum temperature of the hot reservoir, if the heat engine takes 300 J heat from the hot reservoir and delivers 180 J heat to the cold reservoir per cycle, is ____________ K.

When a gas filled in a closed vessel is heated by raising the temperature by 1$$^\circ$$C, its pressure increases by 0.4%. The initial temperature of the gas is ___________ K.

A steam engine intakes 50 g of steam at 100$$^\circ$$C per minute and cools it down to 20$$^\circ$$C. If latent heat of vaporization of steam is 540 cal g^$$-$$1, then the heat rejected by the steam engine per minute is __________ $$\times$$ 10³ cal.

(Given : specific heat capacity of water : 1 cal g^$$-$$1 $$^\circ$$C^$$-$$1)

A monoatomic gas performs a work of $${Q \over {4}}$$ where Q is the heat supplied to it. The molar heat capacity of the gas will be ______________ R during this transformation. Where R is the gas constant.