Question

A pressure cooker of volume $10$ litres contains an ideal gas at atmospheric pressure ${10}^5$ Pa and temperature of $27°C$. It has a whistle which has an area of $0.1c{m}^2$ and mass of $100gm$. To what temperature should it be heated so that the whistle is just lifted up?

• A. $470K$
• B. $600K$
• C. $580K$
• D. $500K$

Answer 1

The correct option is B $600K$

Given, $V_1=10l,P={10}^5,T_1={27}^{o}C,m=100g,A=0.1cm$

Using the ideal gas equation, $pv=nRT$
So, $P_2{V}_2=nR{T}_2{T}_2=\frac{P_2{V}_2}{nR}...\left(1\right)$

Similarly as $P_1{V}_1=nR{T}_{1}n=\frac{P_1{V}_1}{R{T}_1}=\frac{{10}^5\times V}{R\times 300}$

Now the pressure in cooker = $P_2=P_0+\frac{mg}{A}={10}^5+\frac{100\times {10}^{-3}\times 10}{0.1\times {10}^{-4}}{P}_2=2\times {10}^{5}Pa$

Using $P_2$ and $n$ values in eq.(1)
$T_2=\frac{2\times {10}^5\times V\times R\times 300}{R\times {10}^5\times V}{T}_2=600K$