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3. Two samples of gas initially at the same temperature and pressure arecompressed from volume V to V/2 one sample is compressed isothermallyand the other adiabatically in which case the pressure will be higher?Explain?

Vaibhav shukla , 7 Years ago
Grade 11
anser 2 Answers
Arun

Last Activity: 7 Years ago

Dear Vaibhav
 
Suppose
Final pressure during adiabatic compression = Pa
Final pressure during isothermal compression = Pi
For isothermal compression
P*V = Pi * (V/2)
Pi = 2P
Similarly
Pa = 2^(gamma) P
Now
Pa/Pi = 2^(gamma)/2
As gamma>1
Hence
Pa/Pi >1
Hence
Pa > Pi
Final pressure during adiabatic compression is higher than that in isothermal compression.
 
Regards
Arun (askIITians forum expert)

Kushagra Madhukar

Last Activity: 4 Years ago

Dear student,
Please find the solution to your problem.
 
Suppose
Final pressure during adiabatic compression = Pa
Final pressure during isothermal compression = Pi
For isothermal compression
P*V = Pi * (V/2)
Pi = 2P
Similarly
Pa = 2^(gamma) P
Now
Pa/Pi = 2^(gamma)/2
As gamma>1
Hence
Pa/Pi >1
Hence
Pa > Pi
Final pressure during adiabatic compression is higher than that in isothermal compression.
 
Thanks for the question.
Regards,
Kushagra

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