An engine takes in 5 moles of air at 20^oC and 1 atm, and compresses it adiabatically to 1/10^th of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be X kJ. The value of X to the nearest integer is________.

Starting at temperature 300 K, one mole of an
ideal diatomic gas ($$\gamma $$ = 1.4) is first compressed
adiabatically from volume V₁ to V₂ = $${{{V_1}} \over {16}}$$. It is
then allowed to expand isobarically to volume 2V₂. If all the processes are the quasi-static then
the final temperature of the gas (in ^oK) is (to the nearest integer) _____.

Three containers C₁, C₂ and C₃ have water at different temperatures. The table below shows the final temperature T when different amounts of water (given in litres) are taken from each containers and mixed (assume no loss of heat during the process) The value of $$\theta $$ (in °C to the nearest integer) is ..........

M grams of steam at 100^oC is mixed with 200 g of ice at its melting point in a thermally insulated container. If it produced liquid water at 40^oC [heat of vaporization of water is 540 cal/g and heat of fusion of ice is 80 cal/g] the value of M is ____