What is correct for an ideal gas undergoing reversible adiabatic expansion regarding temperature –?

(1) Remain same
(2) Increase
(3) Decreases
(4) May increase or decrease
Please give the reason also.

1 Answer
Morgan
Jan 2, 2018

Decreases

Explanation:

Given that the gas undergoes a reversible adiabatic expansion, we know that the energy input into the system by heating is zero, i.e. #Q=0#. Additionally, given that the process is reversible, we know that there is no net change in entropy, i.e. #DeltaS=0#.

We can describe an adiabatic process using the following equation:

#TV^(gamma-1)="constant"#

where #T# is the temperature, #V# is the volume, and #gamma# is the ratio of specific heat capacities #C_P//C_V#.

Because the gas is expanding, we know that #V# increases. Therefore, in order for the product of #T# and #V# to remain constant, #T# must decrease.

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