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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?

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?

Grade:11

2 Answers

Arun
25763 Points
3 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
askIITians Faculty 629 Points
11 months 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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