Standing waves of frequency 5.0 kHz are produced in a tube filled with oxygen at 300 K. The separation between the consecutive nodes is 3.3 cm. Calculate the specific heat capacities C_P and C_V of the gas

Given:

Standing waves of frequency 5.0 kHz are produced in a tube filled with oxygen at 300 K.

The separation between the consecutive nodes is 3.3 cm.

the node separation is given by which is 3.3cm. Therefore,

the frequency of the sound is 5kHz

thus the velocity of sound will be

again,

where R is the gas constant, T is the temperature of the gas in Kelvin scale and M is the molar mass of the gas.

The molar mass of oxygen is

Thus putting in the values in the above expression,

Again,

Therefore, the C_P and C_V for oxygen are and respectively.