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n' moles of an ideal gas undergoes a pro...

n' moles of an ideal gas undergoes a process `AtoB` as shown in the figure. The maximum temperature of the gas during the process will be:

A

`(3P_0V_0)/(2nR)`

B

`(9P_0V_0)/(2nR)`

C

`(9P_0V_0)/(nR)`

D

`(9P_0V_0)/(4nR)`

Text Solution

Verified by Experts

The correct Answer is:
D
Equation of line
`P= -(P_0)/(V_0)+3P_0`

`PV=-(P_0)/(V_0)V^2 +3P_0V=x(says)`
`(dx)/(dV)=0 implies V=(3V_0)/(2) }` here PV product is max
`implies P=(3P_0)/(2)`
Aliter : Since initial and final temperature are equal hence maximum temperature is at middle of line
`PV=nRT`
`implies (((3P_0)/(2))((3V_0)/(2)))/(nR)=T_(max) implies T_(max)=(9V_0P_0)/(4nR)`
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