Consider a diatomic ideal gas composed of 10 moles of atoms. The gas is initiall

Question

Consider a diatomic ideal gas composed of 10 moles of atoms. The gas is initially at a temperature of 200 Kelvin, and a volume of 1 m^3. a. What is the specific heat per mole of the gas when kept at constant volume? b. What is the specific heat per mole of the gas when kept at constant pressure? c. The gas expands adiabatically to triple its original volume. What is the new pressure of the gas after the expansion? d. What is the work done by the gas during the expansion described in part c? e. What is the final energy of the gas after the expansion in part c?

Explanation / Answer

1) specific heat at constant volume =

Q= Cv n T

Where, Constant volume= 3/2 R = 3/2 * 8.314. = 12.5 J/ mol.

No. of gas = 10 mole

Temperature = 200 Kelvin

Q=12.5 * 10* 200 = 25000

2) At constantCpessure = Cp = 5/2 R

Cp= 5/2 * 8.314 = 20.8 J/ mol

Q= n Cp T

= 10 * 20.8 * 200

= 41600 joule Kelvin

3)

Pressure = R * 1/ volume

Triple volume = 3 m3

Pressure = 1/ 3 * 8.314

= 2.77 ATM

4) Work done = - nrtp

= - 10 * 8.314 * 200* 2.77

= -46059

= 46059 J

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