Question

# A container is filled with an ideal diatomic gas to a pressure and volume of P1...

A container is filled with an ideal diatomic gas to a pressure and volume of P1 and V1, respectively. The gas is then warmed in a two-step process that increases the pressure by a factor of three and the volume by a factor of two. Determine the amount of energy transferred to the gas by heat if the first step is carried out at constant volume and the second step at constant pressure. (Use any variable or symbol stated above as necessary.)

Q=?

Solution:

Given,

Initial values, P1 and V1, Using ideal gas equation

T1 = P1V1/nR .

Step 1 : Constant volume, Pressure is increased to 3P1

T2 = 3P1V1/nR .

The heat energy added in this step, Cv = 5/2R for diatomic

Q1 = nCv T

= n[5/2]R*[3P1V1 - P1V1]/nR

= 5P1V1.

Step 2: Constant pressure, Volume increased to 2V1

T3 = 3P1(2V1)/nR = 6P1V1/nR

The heat energy added in this step Cp = 7/2R for diatomic,

Q2 = nCp T

= n[7/2]R[6P1V1 - 3P1V1]/nR

= 10.5P1V1.

Qnet = Q1 + Q2

= 15.5P1V1.

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