Exams › JEE Advanced › Physics

Two cylinders A (thermally insulated walls and piston) and B (maintained at temperature T0) have pistons connected by a massless rod. Both initially contain ideal gas (gamma = 1.5) at pressure P and temperature T0, each in volume V0. Cylinder A contains mass m of gas. The piston is slowly released and moves until cylinder A's gas volume becomes V0/2. What is the mass of gas in cylinder B?

1. 2*sqrt(2) m
2. 3*sqrt(2) m
3. sqrt(2) m
4. none

Correct answer: 3*sqrt(2) m

Solution

A compresses adiabatically to V0/2: PA' = P*2^gamma = P*2¹.5 = 2*sqrt(2)*P. B expands isothermally to 3*V0/2: PB' = P*V0/(3*V0/2) = 2P/3. At equilibrium PA' = PB': 2*sqrt(2)*P_A_initial = (2/3)*P_B_initial. Since initial pressures are equal, this gives a contradiction unless we use the mass relation: PB_initial/PA_initial = mB/m. Setting PA' = PB': 2*sqrt(2)*P = (2P/3)*(mB/m) is wrong framing. The correct approach: initial PA=PB=P (both same T and V, different masses means different pressures — wait, rereading: same T, same V, same P but different masses means same molar amounts... Let me re-read: 'cylinder A contains m gm at P and T0', 'cylinder B contains identical gas at T0 but different mass, volume V0, and we are told same initial pressure P'. So nA = PV0/RT0 = nB? Only if masses are same. The problem says 'different mass' so they may have different pressures initially — or the piston is held in place so they can have different pressures. At equilibrium: PA' = PB' (piston free). PA' = P*(2)¹.5 = 2*sqrt(2)*P (adiabatic for A). For B: isothermal, PB_initial*V0 = PB'*(3V0/2), so PB' = (2/3)*PB_initial. Setting equal: 2*sqrt(2)*P = (2/3)*PB_initial => PB_initial = 3*sqrt(2)*P. Since PB_initial = mB*R*T0/(M*V0) and P = m*R*T0/(M*V0): mB/m = PB_initial/P = 3*sqrt(2). So mB = 3*sqrt(2)*m.

Related JEE Advanced Physics questions

• Consider an ideal diatomic gas with molecules of mass 'm' at an absolute temperature T. Let V represent the root mean square speed of the molecules, ignoring vibrational energy contributions. Which statement is incorrect?
• The average kinetic energy of a single atom is calculated as (3/2)kT, where k = 1.38 × 10⁻²³ J/K and T = 160 K. What is the resulting value?
• Two non-reactive monatomic ideal gases have their atomic masses in the ratio 2:3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4:3. The ratio of their densities is
• A gas is enclosed in a container at pressure P and absolute temperature T. If k is the Boltzmann constant, the number of gas molecules per unit volume is:
• An ideal gas is in thermodynamic equilibrium at fixed temperature and pressure. A molecule of the gas has n degrees of freedom. Let Uₙ denote the molar internal energy and vₙ denote the speed of sound in the gas when the degrees of freedom are n. Which of the following statements is correct?
• In a mixture of argon and nitrogen gases at room temperature, consider a single collision between one argon molecule and one nitrogen molecule. Which of the following outcomes are physically possible?

⚔️ Practice JEE Advanced Physics free + battle 1v1 →