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.
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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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