1.

One mole of ideal monatomic gas is carried through the reversible cyclic process as shown in figure. Calculate the max temperature attained by the gas during the cycle.

Answer»

`(25)/(8)((P^(@)V^(@))/(R))`
`-(25)/(8)((P^(@)V^(@))/(R))`
`(35)/(8)((P^(@)V^(@))/(R))`
`-(35)/(8)((P^(@)V^(@))/(R))`

Solution :BC is a straight line & equation can be obtained by using
`(y-y_(1)) = (Y_(2)-Y_(1))/(x_(2)-x_(1))(x-x_(1))`
`(P-3P^(@))=(P^(@)-3P^(@))/(2V^(@)-V_(@))(V-V^(@)) implies (P-3P^(@)) =-(2P^(@))/(V^(@))(V-V^(@)) ""…..(1)`
Replacing P by using `P=(RT)/(V)` in equation (1)
`((RT)/(V)-3P^(@))=-(2P^(@))/(V^(@)) (V-V^(@)) implies T=(2P^(@)V(V-V^(@)))/(V^(@)R) + (3P^(@)V)/(R)`
For T to be maximum
`(dT)/(DV)=0`
`(dT)/(dV) =-(2P^(@)(2V-V^(@)))/(V^(@)R)+ (3P^(@))/(R) =0 implies V=(5)/(4)V^(@)`
`T_("max")=-(2P^(@)xx(5)/(4)V^(@)((5)/(4)V^(@)-V^(@)))/(V^(@)R)+(3P^(@)(5)/(4)V^(@))/(R)=(25)/(8)((P^(@)V^(@))/(R))`


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