Question

An empty pressure cooker of volume $10$ liters contains air at atmospheric pressure ${10}^{5}Pa$ and temperature of ${27}^{o}C$. It contains a whistle which has area of $0.1c{m}^2$ and weight of $100gm$. What should be the temperature of air inside so that the whistle is just lifted up?

Answer 1

Mass of the whistle $m=100$ gm $=0.1kg$

Area of the whistle $A=0.1c{m}^2={10}^{-5}{m}^2$

Initial temperature of the air $T_1={27}^{o}C=300K$

Let the pressure required to lift the whistle be $P$

$\therefore$ $mg=PA$

$\therefore$ $0.1\times 9.8=P\times {10}^{-5}$ $⟹P=0.98\times {10}^5$ Pa

Let the temperature to attain that pressure be $T$

Using $\frac{P_o}{T_1}=\frac{P}{T}$ $(as$ $V=constant)$

$\therefore$ $\frac{{10}^5}{300}=\frac{0.98\times {10}^5}{T}$ $⟹T=294K$

$⟹$ $T=294-273={21}^{o}C$