JEE Main · PhysicsHard

$Two containers of volume V_{1} and V_{2} contain the same ideal gas at pressures P_{1} and P_{2} and temperatures T_{1} and T_{2} respectively. If they are connected, what is the final equilibrium temperature?$

A. $T = \frac{P _{1} V _{1} + P _{2} V _{2}}{\frac{P _{1} V _{1}}{T _{1}} + \frac{P _{2} V _{2}}{T _{2}}}$
B. $T = \frac{\frac{P _{1} V _{1}}{T _{1}} + \frac{P _{2} V _{2}}{T _{2}}}{P _{1} V _{1} + P _{2} V _{2}}$
C. $T = \frac{T _{1} + T _{2}}{2}$
D. $T = \frac{P _{1} V _{1} T _{1} + P _{2} V _{2} T _{2}}{P _{1} V _{1} + P _{2} V _{2}}$

Show correct answer & step-by-step solution

Correct answer: A — $T = \frac{P _{1} V _{1} + P _{2} V _{2}}{\frac{P _{1} V _{1}}{T _{1}} + \frac{P _{2} V _{2}}{T _{2}}}$

Solution

Using conservation of moles n_{1} + n_{2} = n_{f} and the ideal gas law n = P V / R T, we solve for the equilibrium state assuming the system is thermally isolated.