One mole of a ideal gas expands obeying the relation as shown in the P/V diagram. The maximum temperature in this process is equal to
A
P0V0R
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B
3P0V0R
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C
9P0V08R
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D
None
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Solution
The correct option is C9P0V08R From the graph shown the equation of line is P−P0=⎛⎜
⎜
⎜⎝P02−P02V0−V0⎞⎟
⎟
⎟⎠(V−V0) P−P0=−P02V0(V−V0) P=−P0V2V0+3P02 Now we know PV=nRT ⇒(32P0−P0V2V0)V=nRT For maximum temperature dTdV=0⇒32P0−P0VV0=0 V=32V0 Tmax=(32P0−P02V0.32V0)32V0.1nR =34P0.32V0.1R=9P0V08R