Question

An insulated box containing helium gas falls from a balloon 4.5 km above the earth’s surface. Calculate the temperature rise in ^oC of the helium when box hits the ground.

Temperature rise = ____ ^oC

Answer 1

The law of transformation of energy says: decreasing in mechanical energy = increasing of internal energy. So

$$mgh=\frac{3}{2}\frac{m}{M}R\Delta T$$

$$\Delta T=\frac{2}{3}\frac{gMh}{R}=\frac{2}{3}\frac{9.8*0.004*4500}{8.3}=14^{\circ}\rm C$$