Chapter 19: Q. 31 (page 544)

0.10 mol of nitrogen gas follow the two processes shown in
Figure EX19.31. How much heat is required for each?

Short Answer

Expert verified

The heat required for different process are -1000 j and 700 J.

Step by step solution

Arranging the equations

This is an isochoric process, and the heat will be given by

$Q = n C_{v} ∆ T$ , where the temperature difference, role="math" localid="1649081855608" $∆ T = T_{f} - T_{1}$

f denotes final parameters and i denotes intial parameters.

finding the needed heat

For process A:

if the temperature decreased by a factor of 3, the temperature did so as well. So, the temperature difference, $∆ T = - 2 T_{f}$ .

As per the ideal gas law,

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

Therefore, the heat will be

role="math" localid="1649081405766" $Q = - 2 n C_{v} \frac{p_{f} V_{f}}{n R} = \frac{p_{f} V_{f} C_{v}}{R} \dots \dots \dots \dots \dots \dots \dots \dots (1)$

The nitrogen gas has an isochoric heat capacity of 20.8J/mol $\cdot$ K.

So,

role="math" localid="1649081654971" $Q = \frac{- 2 \cdot 10^{5} \cdot 2000 \cdot 10^{- 6} \cdot 20.8}{8.314} = - 1000 J$

For process B:

with the same process of A,

$Q = \frac{2 \cdot 29.1 \cdot 1 \cdot 10^{5} \cdot 1000 \cdot 10^{- 6}}{8.314} = 700 J$

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0.10 mol of nitrogen gas follow the two processes shown in
Figure EX19.31. How much heat is required for each?

Short Answer

Step by step solution

Arranging the equations

finding the needed heat

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0.10 mol of nitrogen gas follow the two processes shown inFigure EX19.31. How much heat is required for each?

Short Answer

Step by step solution

Arranging the equations

finding the needed heat

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Torque and Rotational Motion

Famous Physicists

Nuclear Physics

Thermodynamics

Turning Points in Physics

Atoms and Radioactivity

Study anywhere. Anytime. Across all devices.

0.10 mol of nitrogen gas follow the two processes shown in
Figure EX19.31. How much heat is required for each?