Consider n moles of a gas, initially confined within a volume V and held at temperature T. The gas is expanded to a total volume aV, where a is a constant, by (a) a reversible isothermal expansion and (b) removing a partition and allowing a free expansion into the vacuum. Both cases are illus- trated in Fig. 14.9. Assuming the gas is ideal, derive an expression for the change of entropy of the gas in each case.
Consider n moles of a gas, initially confined within a volume V and held at temperature T. The gas is expanded to a total volume aV, where a is a constant, by (a) a reversible isothermal expansion and (b) removing a partition and allowing a free expansion into the vacuum. Both cases are illus- trated in Fig. 14.9. Assuming the gas is ideal, derive an expression for the change of entropy of the gas in each case.
Related questions
Question
Ideal gas case only please
Transcribed Image Text:Consider n moles of a gas, initially confined within
a volume V and held at temperature T. The gas
is expanded to a total volume aV, where a is a
constant, by (a) a reversible isothermal expansion
and (b) removing a partition and allowing a free
expansion into the vacuum. Both cases are illus-
trated in Fig. 14.9. Assuming the gas is ideal,
derive an expression for the change of entropy of
the gas in each case.
(a)
(b)
V
gas
(a-1)V
partition
V
(a-1)V
gas
vacuum
Fig. 14.9 Diagram showing n moles of gas, initially
confined within a volume V.
Repeat this calculation for case (a), assuming that
the gas obeys the van der Waals equation of state
n²a
(p+ ²) (V - nb) = nRT.
(14.55)
Show further that for case (b) the temperature of
the van der Waals gas falls by an amount propor-
tional to (a
1)/a.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 5 images
