Chapter 19: Q 32. (page 544)

A monatomic gas follows the process 1S 2S 3 shown in
Figure EX19.32. How much heat is needed for (a) process 1S 2
and (b) process 2S 3?

Short Answer

Expert verified

The heat needed for process (a) is 150 J and for process (b) -90 J.

Step by step solution

Discussion

The heat needed for an isochoric/isobaric process is

$Q_{\frac{p}{v}} = n C_{\frac{p}{v}} ∆ T$

Process $1 \to 2$ is isobaric. Therefore, if the volume is tripled, the temperature will also be tripled. $\frac{V}{T}$ remains constant in an isobaric process. The change in temperature is $∆ T_{1 \to 2} = 2 T_{1}$ .

As the process $2 \to 3$ is a process going back to same isotherm,

$∆ T_{2 \to 3} = - 2 T_{1}$

Finding of heat required

From the ideal gas law,

$p V = n R T n = \frac{p V}{R T}$

In state 1,

$n = \frac{p_{1} V_{1}}{R T_{1}}$

Then, the heat needed for each isobaric process,

$Q_{p} = n C_{p} ∆ T = \frac{p_{1} V_{1}}{R T_{1}} \cdot C_{p} \cdot 2 T_{1} = \frac{2 p_{1} V_{1} C_{p}}{R}$

Putting the numeric values,

$Q_{p} = \frac{2 \cdot 3 \cdot 10^{5} \cdot 100 \cdot 10^{- 6} \cdot 20.8}{8.314} = 150 J$

This result in an isochoric process will be

$Q_{v} = - \frac{Q_{v}}{γ} = \frac{150}{1.67} = - 90 J$

The heat at the beginning will be

role="math" localid="1649083337274" $Q_{v} = n C_{v} ∆ T Q_{v} = \frac{p_{1} V_{1}}{R T_{1}} \cdot C_{v} \cdot (- 2 T_{1}) = \frac{- 2 p_{1} V_{1} C_{v}}{R} = \frac{- 2 \cdot 3 \cdot 10^{5} \cdot 100 \cdot 10^{- 4} \cdot 12.5}{8.314} = - 90 J$

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A monatomic gas follows the process 1S 2S 3 shown in
Figure EX19.32. How much heat is needed for (a) process 1S 2
and (b) process 2S 3?

Short Answer

Step by step solution

Discussion

Finding of heat required

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A monatomic gas follows the process 1S 2S 3 shown inFigure EX19.32. How much heat is needed for (a) process 1S 2and (b) process 2S 3?

Short Answer

Step by step solution

Discussion

Finding of heat required

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Force

Kinematics Physics

Solid State Physics

Magnetism and Electromagnetic Induction

Wave Optics

Electricity

Study anywhere. Anytime. Across all devices.

A monatomic gas follows the process 1S 2S 3 shown in
Figure EX19.32. How much heat is needed for (a) process 1S 2
and (b) process 2S 3?