TV5/3-1 = T2 ((2)V)5/3-1
T = T2(22/3)
300/(22/3) = T2
2R/(2/3) (T2-T)
At 27 degree C two moles of an ideal monoatomic gas occupy a volume V. The gas expands adiabatically to volume 2V
calculate the final temp, change in internal energy and work done.
Point!
its not given that Constant Ext. Pressure or nethin lyk dat,
Then v can take REVERSIBLE, jus lyk IITIM... took
hmm.......
T1=300K. V1=V. V2=2V. T2=?
mnoatomic => Cv=3/2, Cp=5/2 , γ=5/3
TVγ-1 = constant.
300.V2/3 = T2. (2V)2/3
=> [300/T2] = 3√4
=> T2 = 300/ 3√4 K.
ΔU= nCvΔT. = 2X3/2X (300 - 300/3√4)
= 3.(300 - 300/3√4)
work done = nR(T1-T2)/(γ-1) all the terms we know already.
FOR TEMPERATURE USE
T1VIγ-1=T2V2γ-1
WE GET P1=23/5P2
AND 22/5T1=T2
T1=300K
SO
300 X 22/5=T2
ΔE =nCvdt
=3/2 x 2 x R x (300 X 22/5-300)
as it is adiabatic so ΔQ=0
by applying ΔE=ΔQ-ΔW
we can find the work done