Use the following to answer the question:
-An ideal gas initially at 100ºC and pressure P₁ = 250 kPa occupies a volume V₁ = 4.5 L.It undergoes a quasistatic,isothermal expansion until its pressure is reduced to 150 kPa.How much heat enters the gas during this process? R = 8.314 J/mol·K = 8.206 L·atm/mol·K.

Question

Use the following to answer the question:

-An ideal gas initially at 100ºC and pressure P₁ = 250 kPa occupies a volume V₁ = 4.5 L.It undergoes a quasistatic,isothermal expansion until its pressure is reduced to 150 kPa.How much heat enters the gas during this process? R = 8.314 J/mol·K = 8.206 L·atm/mol·K.

Quizplus · Accepted Answer

We can use the formula for the work done in an isothermal process of an ideal gas:
W = nRT ln(V₂/V₁)
where n is the number of moles of the gas, R is the gas constant, T is the temperature, V₁ is the initial volume, and V₂ is the final volume.
Since the process is quasistatic and isothermal, the temperature remains constant at 100ºC = 373.15 K.
So we have:
W = nRT ln(V₂/V₁) = (1 mol)(8.314 J/mol·K)(373.15 K) ln(4.5 L/6.75 L) = -575 J 
The negative sign indicates work done by the gas, so the heat entering the gas is:
Q = -W = 575 J, which is closest to choice C.

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