Consider two cylinders of gas identical in all respects except that one contains

Question

Consider two cylinders of gas identical in all respects except that one contains oxygen O_2 and the other helium He. Both cylinders initially contain the same volume of gas at 0 degree C and 1 atm of pressure and are closed by a movable piston at one end. Both gases are now compressed adiabatically to one-third their original volume. Which gas will show the greater temperature increase? the He the O_2 Neither; both will show the same increase. It is impossible to tell from the information given. Which gas will show the greater pressure increase? the He the O_2 Neither; both will show the same increase. It is impossible to tell from the information given.

Explanation / Answer

We know that for the adiabatic conditon

PVr =constant then P =Constant/Vr

Here r is the ration of specific heats at cosntat pressure to constant volume, therefore the diffrence in the final pressure will be due to the r for different atoms

The gamma value varies for helium it is 1.66 for oxygen it is 1.4

Therefore the final pressure will be larger will be oxygen (O2)

Simialrly we know that PV =nRT

Here p and T are directly proportinal then oxygen will show greater temperature increase

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