Question

A container is filled with an ideal diatomic gas to a pressure
and volume of *P*_{1} and *V*_{1},
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=?

Answer #1

**Solution:**

Given,

Initial values, P_{1} and V_{1}, Using ideal gas
equation

T_{1} = P_{1}V_{1}/nR .

Step 1 : Constant volume, Pressure is increased to
3P_{1}

T_{2} = 3P_{1}V_{1}/nR .

The heat energy added in this step, C_{v} = 5/2R for
diatomic

Q_{1} = nC_{v}T

= n[5/2]R*[3P_{1}V_{1} -
P_{1}V_{1}]/nR

= 5P_{1}V_{1}.

Step 2: Constant pressure, Volume increased to
2V_{1}

T_{3} = 3P_{1}(2V_{1})/nR =
6P_{1}V_{1}/nR

The heat energy added in this step C_{p} = 7/2R for
diatomic,

Q_{2} = nC_{p}T

= n[7/2]R[6P_{1}V_{1} -
3P_{1}V_{1}]/nR

= 10.5P_{1}V_{1}.

the total Heat added is,

Q_{net} = Q_{1} + Q_{2}

**= 15.5P _{1}V_{1}.**

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