There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K. If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at 600 K, at steady state the pressure in the vessels will be (in kPa).

Solution & Explanation

Related Formula

Ideal Gas Law:

n = (PV)/(RT)

Conservation of moles: n₁ + n₂ = nf

Core Logic

Let the volume of the smaller vessel be V₁ = V, then the volume of the larger vessel is V₂ = 2V. Initial moles in large vessel:

n₂ = (8 × 2V)/(R × 1000) = (16V)/(1000R)

Initial moles in small vessel:

n₁ = (7 × V)/(R × 500) = (14V)/(1000R)

Total total initial moles:

ntotal = n₁ + n₂ = (30V)/(1000R)
Step 1: Connect Vessels to Dynamic Equilibrium

When connected, the total final volume is Vf = V + 2V = 3V. The final temperature is Tf = 600 K. Using mole conservation:

(30V)/(1000R) = (Pf (3V))/(R × 600) (30)/(1000) = (3Pf)/(600) (30)/(1000) = (Pf)/(200)

Pf = (30 × 200)/(1000) = 6 kPa

Dual vessel gas flow schema
Dual vessel gas flow schema

Pattern Recognition

Connecting chambers preserves the net mass/moles (Σ nᵢ = constant). Keep everything relative to a common volume multiplier V to easily cancel terms.

Chapter Mix

Class 11 Physics: Kinetic Theory

Reference Study Guides

Kinetic Theory

More Kinetic Theory Previous-Year Questions — Page 6

Q31 jee_main_2024_31_jan_morning Kinetic Energy Of Gas Molecules
The parameter that remains the same for molecules of all gases at a given temperature is :
  • A. kinetic energy
  • B. momentum
  • C. mass
  • D. speed

Solution

Related Formula
KE = (f)/(2)kT
Core Logic

The average translational kinetic energy of any gas molecule depends only on the absolute temperature of the gas and is independent of the nature or mass of the gas.

For 1 mole of any ideal gas, the average translational kinetic energy is (3)/(2)RT. Therefore, at a given temperature, the kinetic energy parameter is uniform across all ideal gases.

Pattern Recognition

Temperature is directly proportional to average translational kinetic energy. If T is constant, KE is constant for all gases regardless of mass.

Chapter Mix

Class 11 Physics: Kinetic Theory

More Kinetic Theory Questions — jee_main_2025_04_april_evening

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