Question

In a closed vessel, at a constant volume, URMS of a real gas is increased from $5\times {10}^4$cm/s to $10\times {10}^4$cm/s. Which statement is true:

• A. Temperature is doubled after heating the gas
• B. Pressure will be four time after heating the gas.
• C. Volume will be 3 times after the gas is heated
• D. Pressure is doubled after heating the gas.

Answer 1

The correct option is A Temperature is doubled after heating the gas

$M_{RMS}=\sqrt{\frac{3RT}{M}}$

$M_{RMS}\propto \sqrt{\frac{RT}{M}}\Rightarrow \frac{M_{RM{S}_1}}{M_{RM{S}_2}}=\sqrt{\frac{T_1}{T_2}}$

$\frac{5\times {10}^4}{10\times {10}^4}=\sqrt{\frac{T_1}{T_2}}\Rightarrow \frac{T_1}{T_2}=\frac{1}{4}$