Exams › JEE Advanced › Physics

An ideal gas undergoes isothermal expansion from volume V1 to V2 (V2 > V1) starting at pressure P1. It is then compressed adiabatically back to its original volume V1, reaching final pressure P3. If W is the total work done by the gas in both processes, which statement is correct?

1. P3 > P1, W > 0
2. P3 < P1, W < 0
3. P3 > P1, W < 0
4. P3 = P1, W = 0

Correct answer: P3 > P1, W < 0

Solution

During isothermal expansion (V1->V2 at T_initial), work done by gas W_iso = nRT*ln(V2/V1) > 0. After isothermal step, gas is at T_initial and pressure P1*V1/V2 < P1. During adiabatic compression back to V1: temperature rises above T_initial (since no heat is released), so final pressure P3 = nRT_f/V1 > nRT_initial/V1 = P1. Work done BY gas in adiabatic compression = -nCv*(T_f - T_initial) < 0 (work is done ON the gas). The adiabat is steeper than the isotherm on a PV diagram, so |W_adi| > |W_iso|. Total W = W_iso + W_adi < 0.

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 →