Work done by a Carnot engine operating between temperatures $$127^{\circ} \mathrm{C}$$ and $$27^{\circ} \mathrm{C}$$ is $$2 \mathrm{~kJ}$$. The amount of heat transferred to the engine by the reservoir is :

Given below are two statements:

Statement I: If heat is added to a system, its temperature must increase.

Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase.

In the light of the above statements, choose the correct answer from the options given below

The temperature of an ideal gas is increased from $$200 \mathrm{~K}$$ to $$800 \mathrm{~K}$$. If r.m.s. speed of gas at $$200 \mathrm{~K}$$ is $$v_{0}$$. Then, r.m.s. speed of the gas at $$800 \mathrm{~K}$$ will be:

A body cools in 7 minutes from $$60^{\circ} \mathrm{C}$$ to $$40^{\circ} \mathrm{C}$$. The temperature of the surrounding is $$10^{\circ} \mathrm{C}$$. The temperature of the body after the next 7 minutes will be: