The equation of state for a certain gas under isothermal conditions is
PV = 31.2,
Where the units are SI. The work done by this gas as its volume increases isothermally from 1 L to 10 L is approximately

Question

Quizplus · Accepted Answer

Under isothermal conditions, we have:

PV = nRT,

where n is the number of moles of gas, R is the gas constant, and T is the temperature.

Since the temperature is constant, we can express the pressure as a function of the volume:

P = nRT/V.

Substituting this into the work formula, we get:

W = ∫PdV = ∫nRT/V dV = nRT ln(V2/V1).

We are given that PV = 31.2, so we can solve for nRT:

nRT = PV = 31.2.

Substituting this back into the work formula, we get:

W = 31.2 ln(10/1) ≈ 71.8 J.

Therefore, the best choice is C.

The Equation of State for a Certain Gas Under Isothermal