Question

When one mole of an ideal gas is compressed reversibly and adiabatically to half of its original volume, the temperature of the gas increases from 273 K to 433 K. Calculate C_V for this gas, assuming that it is temperature independent.

Is this gas monatomic or diatomic?

Answer 1

Hello!

Greetings of the day!

As we know for adiabatic reversible compression of a gas,

.....................(1)

Also,

.......................(2)

C_p = C_v + R...................(3)

So substituting,

T^f = 433 K

Tⁱ = 273 K

2V^f = Vⁱ

in (1), we get

= 1.23

Using the above obtained value of γ and equations (2) and (3) we get,

R= 8.314 J K^-1 mol^-1

C_v = 36.15 J K^-1 kg^-1

As we can see  = 1.23 .

Thus we can say that the gas is diatomic.