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THERMODYNAMICS: ADIABATIC PROCESSES

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The notes are for the thermodynamics in chemistry and chemical engineering. They explain the adiabatic processes in detail and also they consists of worked examples and self test exercises

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  • November 13, 2022
  • 10
  • 2022/2023
  • Class notes
  • Dr ray
  • All classes
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Unit 5
The internal energy of an ideal gas
Joule experiment
Setup: Two flasks (A and B) are totally immersed in a water bath, which is
surrounded by a thermally insulated wall. A thermometer is in contact with the water
bath.
 flask A contains gas at high pressure and separated by valve (in closed
position) from flask B, which is completely evacuated
 Valve is opened, and gas would expand against the vacuum while
temperature is monitored




Result: No temperature change was observed
Conclusion: q= 0 and w = 0 (dw = -PextdV , Pext = 0)


ΔU = q + w = 0
(1)
A total differential (dU) can be setup for this system that evaluated volume change
and temperature change:
𝜕𝑈 𝜕𝑈
𝑑𝑈 = ( ) 𝑑𝑉 + ( ) 𝑑𝑇 = 0
𝜕𝑉 𝑇 𝜕𝑇 𝑉
(2)

, Effect on U when
Step 1: changing V while keeping T constant
Step 2: changing T while keeping V constant



U

(1) dU = 0

(2) T

V




Rearrangement of equation 2:
𝜕𝑈 𝜕𝑈 𝜕𝑇
( ) = −( ) ( )
𝜕𝑉 𝑇 𝜕𝑇 𝑉 𝜕𝑉 𝑈
(3)
From Joule experiment: temperature did not change on expansion of gas, therefore
𝜕𝑇
( ) =0
𝜕𝑉 𝑈


This implies from equation 3 that:
𝜕𝑈
( ) =0
𝜕𝑉 𝑇


For an ideal gas, the internal energy is independent of volume.
𝜕𝑈
( ) = 𝜋𝑇
𝜕𝑉 𝑇
𝜋 𝑇 = internal pressure= 0 for ideal gas

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