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One mole of a gas changed from its initi...

One mole of a gas changed from its initial state (15L,2 atm) to final state (4L,10 atm) reversibly. If this change can be represented by a straight line in P - V curve maximum temperature (approximate), the gas attained is `x xx10^(2) K.` Then find the value of x.

Text Solution

Verified by Experts

The correct Answer is:
7
Equation of line
`P-2=(10-2)/(4-15)(V-15)`
`P-2=(8)/(11)(V-15)`
`P=2-(8V)/(11)+(15xx8)/(11)`
`P=((142)/(11)-(8V)/(11))`

`f(T)=(1)/(nR)((142V)/(11)-(8V^(2))/(11))`
`(d(F(T)))/(dV)=(1)/(nR)((142)/(11)-(8V^(2))/(11))=0`
`V=(142)/(11xx16)=8.875`
`P=(142)/(11)-(8)/(11)xx(8.875)/(16)=(71)/(11)`
`T_("Max")=(PV)/(nR)=(71)/(11)xx(142)/(16xx0.0821)=700`
`=7xx10^(2)K`
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Knowledge Check

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