Two moles of an ideal gas have an initial Kelvin temperature Tᵢ and absolute pressure Pᵢ.The gas undergoes a reversible isothermal compression from an initial volume Vᵢ to a final volume 0.5Vᵢ.
-How much heat is exchanged with the environment? If heat is exchanged,is it absorbed or released?

Question

Quizplus · Accepted Answer

Since the process is reversible, the gas can be considered to be in thermal equilibrium with the environment throughout the process. Therefore, the temperature of the gas remains constant and the change in internal energy of the gas is zero. By the first law of thermodynamics, the amount of heat exchanged with the environment is equal to the work done on the gas: Q = -W.

The work done on the gas can be calculated using the formula for reversible isothermal compression:

W = nRTᵢ ln(Vᵢ/0.5Vᵢ) = -nRTᵢ ln 2

Substituting the given values, we get:

W = 2 × R × Tᵢ × ln 2

Q = -W = -2 × R × Tᵢ × ln 2

Since ln 2 is a positive number, Q is negative, which means that heat is released from the system to the environment. The correct answer is therefore (A) PᵢVᵢ (ln 2), released.

Two Moles of an Ideal Gas Have an Initial Kelvin