Chapter 3: Q. 3.27 (page 112)

What partial-derivative relation can you derive from the thermodynamic identity by considering a process that takes place at constant entropy? Does the resulting equation agree with what you already knew? Explain.

Short Answer

Expert verified

The relation that can be derived from the thermodynamic identity is $P = - {(\frac{d U}{d V})}_{N, S}$ .

The derived equation agrees with the first law of thermodynamics.

Step by step solution

Given Information

The thermodynamic identity is:

$d U = T d S - P d V$

The process is taking place at constant entropy.

Hence, $d S = 0$

Calculation

Since the process is taking place at constant entropy, the thermodynamic identity can be written as:

$d U = T d S - P d V d U = - P d V P = - {(\frac{d U}{d V})}_{N, S}$

This is the derived relation.

From the relation, it can be seen that the volume change is fully responsible for the energy shift. As a result, there is no heat transfer into or out of the system. Heat flows until equilibrium is reached, resulting in a rise in entropy. As a result, the equation follows the first law of thermodynamics.

Final answer

The derived relation is $P = - {(\frac{d U}{d V})}_{N, S}$ . It agrees with the first law of thermodynamics.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

What partial-derivative relation can you derive from the thermodynamic identity by considering a process that takes place at constant entropy? Does the resulting equation agree with what you already knew? Explain.

Short Answer

Step by step solution

Given Information

Calculation

Final answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Physics of Motion

Work Energy and Power

Kinematics Physics

Electric Charge Field and Potential

Further Mechanics and Thermal Physics

Modern Physics

Study anywhere. Anytime. Across all devices.