[UPSC CSE 2000] Thermodynamics (Q143, 20M)

A tank whose capacity is 0.1\text{ m}^3 contains helium at a pressure of 10\text{ atmospheres} and a temperature of 20^\circ\text{C}. A rubber weather balloon is inflated with this helium.

(i) When the pressure of helium in the balloon is 1\text{ atmosphere}, its temperature is -40^\circ\text{ C}. Find the volume of the balloon.

(ii) Eventually the helium in the balloon absorbs heat from the air around ii and returns to 20^\circ\text{ C}. Find the volume of the balloon at this time.