A monatomic ideal gas with an initial pressure of 500 kPa and an initial volume of 1.80 L expands isothermally to a final volume of 5.20 L. How much work is done on the gas in this process?
A) 955 J
B) 900 J
C) 875 J
D) 1570 J
E) 1700 J

Question

Quizplus · Accepted Answer

In an isothermal process, the temperature remains constant. Therefore, we can use the following equation to calculate the work done on the gas:
W = -nRT ln(Vf/Vi)
where n is the number of moles of gas, R is the gas constant (8.31 J/mol·K), T is the temperature (in K), Vi is the initial volume and Vf is the final volume.
Since the gas is monatomic, we can use the ideal gas law to find the number of moles:
PV = nRT
n = PV/RT
Substituting this into the first equation, we get:
W = -PV ln(Vf/Vi)
W = -(500 kPa)(1.80 L) ln(5.20 L/1.80 L)
W = -955 J
Since the gas is expanding, the work done on the gas is negative. Therefore, the answer is 955 J, which corresponds to choice A.

A Monatomic Ideal Gas with an Initial Pressure of 500