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Question
Two moles of an ideal gas is heated at constant pressure of one atmosphere from 27oC to 127oC. If Cv,m=20+10−2T JK−1 mol−1, then q and △U for the process are respectively:
Two moles of an ideal gas is heated at constant pressure of one atmosphere from 27oC to 127oC. If Cv,m=20+10−2T JK−1 mol−1, then q and △U for the process are respectively:
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Solution
The correct option is A 6362.8 J, 4700 J
We have to calculate q, heat given and work.
Work here will be w=−nR △T
putting the values we get
=−2×8.314×100=−1662.8 J
Also we know,
△U=n∫400300Cv,mdT=2×∫400300(20+10−2T)dT
putting the values we get,
=2[20×100+10−22(4002−3002)]=4700 J
from first law of thermodynamics we know
ΔU=q+w
Putting the values, we get ;
4700=q−1662.8
∴ q=6362.8 J.
We have to calculate q, heat given and work.
Work here will be w=−nR △T
putting the values we get
=−2×8.314×100=−1662.8 J
Also we know,
△U=n∫400300Cv,mdT=2×∫400300(20+10−2T)dT
putting the values we get,
=2[20×100+10−22(4002−3002)]=4700 J
from first law of thermodynamics we know
ΔU=q+w
Putting the values, we get ;
4700=q−1662.8
∴ q=6362.8 J.
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