n' moles of an ideal gas undergoes a process `AtoB` as shown in the figure. The maximum temperature of the gas during the process will be:

Options

A. `(9P_(0)V_(0))/(4nR)`
B. `(3P_(0)V_(0))/(2nR)`
C. `(9P_(0)V_(0))/(2nR)`
D. `(9P_(0)V_(0))/(nR)`

Answer

A

Explanation

Line equation for givengraph `(y=mx+c)`
`P=-(P_(0))/(V_(0))V+3P_(0)=(nRT)/(V)`
`T=(1)/(nR)[-(P_(0))/(V_(0))V^(2)+3P_(0)V]rarr` (1)
To get max temp `(dT)/(dV)=0`
`rArrV=(3V_(0))/(2) &` sub in eq (1) for `T_("max")`