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  • One mole of an ideal monoatomic gas istaken along the path ABCA as shown inthe PV diagram. The maximumtemperature attained by the gas alo

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 : (1) 25 P Vo o 16 R (2) 25 P Vo o 8 R (3) 25 P Vo o 4 R (4) 5 P Vo o 8 R

Answers (1)

lets see the given diagram 

equation of given path is 

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}/Rv_{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}

 

Posted by

Safeer PP

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