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MHT CET202523 Apr 2025Morning ShiftPhysicsKinetic Theory of GasesActual

The pressure 'P', volume 'V' and temperature 'T' of a gas in a jar 'A' and the gas in other jar ' B ' is at pressure ' 2 P ', volume ^ V 4 ' and temperature ^ T 4 ^ . Then the ratio of the number of molecules in jar A and jar B will be

Options

  1. A1: 1
  2. B1: 2
  3. C2: 1
  4. D4: 1

Correct answer

B. 1: 2

Step-by-step solution

The ideal gas law states PV = NkT , so N = PV kT . For jar A: P_A = P , V_A = V , T_A = T , yielding N_A = PV kT . For jar B: P_B = 2P , V_B = V 4 , T_B = T 4 , so N_B = (2P)(V/4) k(T/4) = PV/2 kT/4 = PV kT 2 . The ratio is N_A N_B = PV/kT 2PV/kT = 1 2 . Final ratio: 1:2

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