GATE Mechanical Engineering (ME) 2020 Shift 1 Solved Paper

Question : 13 of 65

Marks: +1, -0

For an ideal gas, the value of the Joule-Thomson coefficient is

Solution:

Joule Thomson coefficient for real gas

µ=(\;{∂ T}/{∂ P})_{h}=\;{1}/{C_{p}}[T(\;{∂ V}/{∂ T})_{P}-V]

.....(1)
For an ideal gas, PV = RT

{T}(\;{∂ {V}}/{∂ {T}})_{P}- {V}

So,

T(\;{∂ V}/{∂ T})_{P} × P=R

(\;{∂ {V}}/{∂ {T}})_{ {P}}=\;{ {R}}/{ {P}} . . . . . .(2)

Putting eqn (2) in eq (1)

µ=\;{1}/{ {C}_{ {p}}}[ {T} × \;{ {R}}/{ {P}}- {V}]

Now, since,

\;{12 {T}}/{ {P}}= {V}

µ=\;{1}/{C_{p}}[V-V]=0

µ=0

(for ideal gas)

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