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An ideal gas (C(P)//C(V)=gamma) is exp...

An ideal gas `(C_(P)//C_(V)=gamma)` is expanded so that the amount of heat transferred to the gas the is equal to the
decrease in its internal energy .
What is the magnitude of work performed by one mole of the gas when its volume increase eight times
if the initinal temperature of the gas is ` 300 K `? `C_(V)` for the gas is `1.5R` .(`R=2 cal//mol//K`)

A

900 cal

B

450 cal

C

1247.7 cal

D

623.8 cal

Text Solution

Verified by Experts

The correct Answer is:
A
`T_(2)=T_(1)((V_(1))/(V_(2)))^(gamma-1//2)=300 xx((1)/(8))^((5)/(3)-1//2)=150 K`
Now, `w= DeltaU - q = 2DeltaU = 2 n C_(v) DeltaT`
`= 2 xx 1 xx 1.5 R xx(150 - 300) = - 900 al.`
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