JEE Mains · Physics · STD 11 - 12 . kinetic theory of gases
One gas of \(n_1\) mole of molecules at temperature \(T_1\), volume \(V_1\), and pressure \(P_1\), and another gas of \(n_2\) mole of molecules at temperature \(T_2\), volume \(V_2\), and pressure \(P_2\), are mixed resulting in pressure \(P\) and volume \(V\) of the mixture. The temperature of the mixture is _____.
- A \((T_1 + T_2)/2\)
- B \(T_1 T_2 PV/(T_2 P_1 V_1 + T_1 P_2 V_2)\)
- C \((T_2 P_1 V_1 + T_1 P_2 V_2)/(T_1 T_2 PV)\)
- D \(|T_1 - T_2|/2\)
Answer & Solution
Correct Answer
(B) \(T_1 T_2 PV/(T_2 P_1 V_1 + T_1 P_2 V_2)\)
Step-by-step Solution
Detailed explanation
From the ideal gas equation, the number of moles of the first gas is \(n_1 = \dfrac{P_1 V_1}{R T_1}\) and the number of moles of the second gas is \(n_2 = \dfrac{P_2 V_2}{R T_2}\). For the mixture, the total number of moles is \(n = n_1 + n_2\). Applying the ideal gas equation…
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