Exams › JEE Advanced › Physics

A thermally insulated rigid container is divided into two equal compartments by a thin membrane. One compartment contains 1 mole of an ideal monoatomic gas at temperature T, and the other is completely evacuated. The membrane is suddenly ruptured, and the gas expands freely and irreversibly to occupy the full container. Find the entropy change of the gas (in J/K). Given: R = 25/3 J/(mol K), ln 2 = 0.7.

1. 25/3
2. 35/6
3. 25/6
4. 50/3

Correct answer: 35/6

Solution

In free expansion into vacuum, the gas does no work (W = 0) and receives no heat (Q = 0, thermally insulated). By the first law, delta U = 0, so temperature is unchanged (ideal gas). The entropy change is calculated using a reversible isothermal path between the same states: delta S = nR ln(V_f/V_i) = 1 * (25/3) * ln(2) = (25/3) * 0.7 = 35/6 J/K.

Related JEE Advanced Physics questions

• A Carnot engine takes in 1000 J of thermal energy from a source at 127°C and expels 600 J of energy to the surroundings in each cycle. What is the engine's efficiency and the temperature of the cold reservoir?
• An ideal gas undergoes adiabatic expansion from an initial condition (Tₐ, V₀) to a final condition (T₆, 5V₀). Another mole of the same gas expands isothermally from a different starting point (T₆, V₀) to the same final point (T₆, 5V₀). If the ratio of specific heats at constant pressure and volume for this gas is γ, what is the value of Tₐ/T₆?
• One mole of a monoatomic ideal gas undergoes an irreversible adiabatic expansion against a constant external pressure of 1 atm. The initial conditions are: pressure = 5 atm and temperature = 300 K. The process continues until the gas pressure equals 2 atm. What is the final temperature (in K)? (R = 2 cal / mol K)
• One mole of NH3 gas (gamma = 1.33) initially at 27 degrees C is expanded reversibly and adiabatically until its volume becomes 8 times the original volume. Which of the following statements is/are correct?
• An ideal monatomic helium gas at pressure P0 and volume V0 is enclosed in a vertical cylinder whose top is open to atmosphere. A frictionless horizontal piston of mass m and cross-section A sits on the gas. A spring of constant k = m*g*A/V0 connects the piston to the upper wall. Initially the system is in equilibrium with the spring unstretched. All processes are adiabatic with gamma = 5/3 for helium. When the piston is displaced slightly from equilibrium and released, its frequency of small oscillations is (1 / (2*pi)) * sqrt(eta * g * A / V0). If atmospheric pressure Pa = m*g/A (so that P0 = 2*m*g/A), find the value of eta.
• An ideal monatomic (Helium) gas at pressure P0 and volume V0 is enclosed in a vertical frictionless cylindrical container with a horizontal piston of mass m and cross-sectional area A. A spring connects the piston to the upper wall; initially the spring is unstretched and the system is in equilibrium. All processes are adiabatic (gamma = 5/3). The piston is pushed down until the gas volume becomes V0/8 and then released from rest. Find the integer K such that the speed of the piston when the spring first returns to its natural (unstretched) length is sqrt(K * P0 * V0 / (64 * m)).

⚔️ Practice JEE Advanced Physics free + battle 1v1 →