A certain ideal gas has molar heat capacity at constant volume CV. A sample of this gas initially occupies a volume V0 at pressure p0 and absolute temperature T0. The gas expands isobarically to a volume 2V0 and then expands further adiabatically to a final volume 4V0. (a) Draw a pV-diagram for this sequence of processes. (b) Compute the total work done by the gas for this sequence of processes. (c) Find the final temperature of the gas. (d) Find the absolute value of the total heat flow /Q /into or out of the gas for this sequence of processes, and state the direction of heat flow.

Short Answer

Expert verified

(a)In the first process pressure remains constant and in the second process it reduced adiabatically.

(b) the total work done by the gas for this sequence of processes is

WT=POVO1+CVR2-22-γ

(c) the final temperature of the gas isT3=TO22-γ

(d) the absolute value of the total heat flow 0 Q 0 into or out of the gas for this sequence of processes isQ=POVOCVR+1

Step by step solution

01

Step 1

ideal gas with heat capacity at constant volume is cv

gas occupies a volume V0 at pressure p0

absolute temperature is T0

gas expands isobarically to a volume= 2V0

expands further adiabatically to a final volume= 4V0

02

Step 2:

(a) pV-diagram for this sequence of processes

The pressure is constant and volume expands to its double value in the first process.in the second process volume increases to four times to its initial volume and it expands adiabatically thus the pressure will decrease exponentially.

(b) the total work done by the gas for this sequence of processes.

For two processes total work done is summation of each work done in both process

WT=Wisobaric+WadiabaticWT=po2VO-VO+CVRPO2VO-P34VOP3=PO2VO3VO

………………………………….(1)

Final pressure related initial pressure by

Put all values in equation 1

WT=PO2VO-VO+CORPO2VO-P34VOWT=poVO1+CVR2-22-γ

Thus, the total work done by the gas for this sequence of processes isWT=poVO1+CVR2-22-γ

03

Step 3

(c) the final temperature of the gas

use ideal gas law for two instant for p and V the final temperature of the gas

T3=T0V3V1p3p1T3=T0V3V1V2V3γT3=TO4V0V02V0V0T3=TO22-γ

Thus, the final temperature of the gas isT3=TO22-γ .

04

Step 4:

(d) the absolute value of the total heat flow 0 Q 0 into or out of the gas for the sequence of processes.

The heat flow Q is given by,

Q=nCVT1-T2Q=POVORTOCV-R2TO-TOQ=POVOCVR+1

Thus, the absolute value of the total heat flow 0 Q 0 into or out of the gas for this sequence of processes is Q=POVOCVR+1 .

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