Ten moles of an ideal monoatomic gas, initially in state a at atmospheric pressure and temperature T(a) = 27°C, is enclosed in a metal cylinder of volume V₀ fitted with a frictionless piston. The gas is suddenly compressed to state b with volume V₀/3. Now, keeping the piston stationary, the cylinder is submerged in a water bath of temperature 11°C until the gas reaches the temperature of the water bath, which is denoted as state c. Finally, while still in the water bath, the piston is brought slowly to its initial position, which is denoted as state f. If R is universal gas constant, then the correct option(s) is/are: [Given: 9^(1/3) = 2.08]
Select all that apply

Question

Ten moles of an ideal monoatomic gas, initially in state a at atmospheric pressure and temperature T(a) = 27°C, is enclosed in a metal cylinder of volume V₀ fitted with a frictionless piston. The gas is suddenly compressed to state b with volume V₀/3. Now, keeping the piston stationary, the cylinder is submerged in a water bath of temperature 11°C until the gas reaches the temperature of the water bath, which is denoted as state c. Finally, while still in the water bath, the piston is brought slowly to its initial position, which is denoted as state f. If R is universal gas constant, then the correct option(s) is/are: [Given: 9^(1/3) = 2.08]

Select all that apply

G1 Physics · Accepted Answer

The sudden adiabatic compression is irreversible. Using energy balance with the final equilibrium pressure and V(b)=V₀/3 gives the temperature change corresponding to ΔU(a→b)=4860R. Cooling at fixed volume takes the gas to 284 K, and the final slow expansion in the bath is isothermal. Since initial temperature is 300 K and final temperature is 284 K, ΔU(total)=10(3R/2)(284−300)=−240R. The source key marks A, B and C as correct.