One mole of an ideal monoatomic gas is taken along the path ABCA as shown in
the PV diagram. The maximum temperature attained by the gas along the
path BC is given by :

Answers (1)
S Sayak

As we have learned

Ideal gas equation -

PV = nRT
 

 

- wherein

T= Temprature

P= pressure of ideal gas

V= volume

n= numbers of mole

R = universal gas constant

 

equation of given path is

 p-3p_{0}=3\frac{p_{0}-3p_{0}}{2v_{0}-v_{0}} 

p-3p_{0}=\frac{2p_{0}}{v_{0}}(v-v_{0})

p= \frac{-2p_{0}}{v_{0}}v+5p_{0}

PV=RT or P=RT/V

\therefore RT/V= (-2p_{0}/v_{0})v^{2}+\frac{5p_{0}}{R}v

for T  to be maximum 

dT/dv= 0  or \frac{-2 p_{0}}{Rv_{0}}2v+5p_{0}/R=0     or     v= 5v_{0}/4

T^{max}= 25/8\frac{p_{0}v_{0}}{R}

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