# 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?

Arun
25750 Points
6 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
3 years ago
Dear student,

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