Question

Two identical vessels contain gases at \(T_0, P_0\). One heated to \(2T_0\). Find pressure \(P\) and number of moles \(n\).

• A. \(p = 2p_0\)
• B. \(p = \frac{4}{3}p_0\)
• C. \(n = \frac{2p_0V_0}{3RT_0}\)
• D. \(n = \frac{3p_0V_0}{2RT_0}\)

Hint:

Use conservation of total moles + ideal gas equation together.

Answer 1

The Correct Option is B

Step 1: Initial moles in each vessel
\[ n_0 = \frac{p_0 V_0}{RT_0} \]

Step 2: After heating one vessel
\[ n_1 = \frac{pV_0}{R(2T_0)},\quad n_2 = \frac{pV_0}{RT_0} \]

Step 3: Total moles conserved
\[ n_1 + n_2 = 2n_0 \] \[ \frac{pV_0}{2RT_0} + \frac{pV_0}{RT_0} = \frac{2p_0V_0}{RT_0} \] \[ \frac{3pV_0}{2RT_0} = \frac{2p_0V_0}{RT_0} \Rightarrow p = \frac{4}{3}p_0 \]

Step 4: Moles in heated vessel
\[ n = \frac{pV_0}{2RT_0} = \frac{2p_0V_0}{3RT_0} \] Final Answer: \[ {(B), (C)} \]