JEE Main20264 April 2026Morning ShiftPhysicsKinetic Theory of GasesActual
One gas of n₁ mole of molecules at temperature T₁ , volume V₁ , and pressure P₁ , and another gas of n₂ mole of molecules at temperature T₂ , volume V₂ , and pressure P₂ , are mixed resulting in pressure P and volume V of the mixture. The temperature of the mixture is _____.
Options
- A(T₁ + T₂)/2
- BT₁ T₂ PV/(T₂ P₁ V₁ + T₁ P₂ V₂)
- C(T₂ P₁ V₁ + T₁ P₂ V₂)/(T₁ T₂ PV)
- D|T₁ - T₂|/2
Correct answer
B. T₁ T₂ PV/(T₂ P₁ V₁ + T₁ P₂ V₂)
Step-by-step solution
From the ideal gas equation, the number of moles of the first gas is n₁ = P₁ V₁ R T₁ and the number of moles of the second gas is n₂ = P₂ V₂ R T₂ . For the mixture, the total number of moles is n = n₁ + n₂ . Applying the ideal gas equation for the mixture: P V = n R T T = P V n R Substituting the values of n₁ and n₂ : T = P V ( P₁ V₁ R T₁ + P₂ V₂ R T₂ ) R T = P V P₁ V₁ T₁ + P₂ V₂ T₂ T = T₁ T₂ P V P₁ V₁ T₂ + P₂ V₂ T₁ Answer: T₁ T₂ PV/(T₂ P₁ V₁ + T₁ P₂ V₂)