Question

‘n’ moles of an ideal gas undergoes a process A→B as shown in the figure. The maximum temperature of the gas during the process will be :

Answer 1

This question is solved by using general gas equation.  The solution of given problem is solved on page and is attached below.Stepwise explanation is given. If you have any confusion or problem, drop a comment in comment box.  I hope this solution will be helpful for you.

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Equation of line AB

y−y1=(y2−y1 )(x−x1)/(x2−x1)

P−P0=2P0−P0(V−2V0)/V02V0

=−P0  (V−2V0)/V0

P=−P0V/V0 V+3P0

PV=−P0V/V0+3P0V

nRT=−P0V/V0+3P0V

T=1 (−P0V0V2+3P0V) /nR

dTdV=0 (For maximum temperature)

−P0 2V/V02V+3P0=0

−P0 2V/V0=−3P0

V=3 V0/2 (Condition for maximum temperature)

Tmax=1nR(−P0/V0×9V²0/4V20+3P0×3V0/2)

Tmax=1nR(−9P0V0/4+9P0V0/2)

=9P0V0/4nR