A vessel that can withstand a pressure of $100 \mathrm{~atm}$ is filled with hydrogen at $27^{\circ}…

A vessel that can withstand a pressure of $100 \mathrm{~atm}$ is filled with hydrogen at $27^{\circ} \mathrm{C}$ up to a pressure of $20 \mathrm{~atm}$. If the vessel is heated, then the temperature at which it explodes is
  1. $500 \mathrm{~K}$
  2. $1000 \mathrm{~K}$
  3. $1500 \mathrm{~K}$
  4. $2000 \mathrm{~K}$

Solution

From ideal gas equation $\begin{aligned} & \mathrm{PV}=\mathrm{nR} T \\ & \frac{\mathrm{P}_1}{\mathrm{P}_2}=\frac{\mathrm{T}_1}{\mathrm{~T}_2} \\ & \mathrm{~T}_2=\frac{\mathrm{P}_2 \mathrm{~T}_1}{\mathrm{P}_1}=\frac{100 \times(27+273)}{20}=1500 \mathrm{~K}\end{aligned}$

Asked in: AP EAMCET 2023 (17 May Shift 2)

Practice more Kinetic Theory of Gases questions on Aicharya