How Is Heat Calculated from Entropy and Temperature Changes in Thermodynamics?

  • Thread starter Thread starter jmcgraw
  • Start date Start date
  • Tags Tags
    Entropy Heat
Click For Summary
SUMMARY

The discussion centers on calculating heat transfer (Q) for an ideal monatomic gas using the relationship between entropy (S) and temperature (T). The user initially applied the formula dQ = T dS, derived from the differential form of entropy, but encountered difficulties in integration. After re-evaluating the approach and integrating from initial to final entropy, they successfully obtained the correct answer for problem #8 in Chapter 21 of Halliday/Resnick/Walker 6th edition. The user seeks a more straightforward method for this calculation.

PREREQUISITES
  • Understanding of thermodynamic principles, specifically the relationship between heat, entropy, and temperature.
  • Familiarity with calculus, particularly integration techniques.
  • Knowledge of ideal gas laws and properties of monatomic gases.
  • Experience with interpreting thermodynamic graphs and charts.
NEXT STEPS
  • Study the derivation of the first law of thermodynamics and its applications in heat transfer.
  • Learn about the Maxwell relations in thermodynamics for alternative methods of calculating heat.
  • Explore the concept of specific heat capacities for different processes (isothermal, adiabatic).
  • Investigate the use of software tools for thermodynamic calculations, such as MATLAB or Python libraries.
USEFUL FOR

This discussion is beneficial for students of thermodynamics, physics educators, and engineers involved in thermal systems who seek to deepen their understanding of heat transfer calculations and thermodynamic principles.

jmcgraw
Messages
70
Reaction score
0
I am given the number of moles of an ideal monotomic gas. I am also given a chart with a graph of temperature plotted as a function of entropy.

One of the questions is: find the heat that was transferred to the gas.

How do I find that? I thought about saying:

dS = dQ/T <=> dQ = T dS

then I found the slope of the graph with respect to S and found the y-intercept. So now I had T in terms of S and I said:

dQ = (mS + b) dS

taking the integral of both sides I found Q and was able to easily integrate from initial entropy to final entropy. But I got the answer wrong. I don't want to do it all over again, unless I am sure this is the right approach. Is there an easier way?

This is problem #8 in Chapter 21 of Halliday/resnick/walker 6th edition.
 
Physics news on Phys.org
O.k. I overcame my sloth and did it again. I got the right answer!

But it seems overly involved. Is there an easier way?
 

Similar threads

Change in entropy of the surroundings in an irreversible process
  • · Replies 14 ·
Replies
14
Views
1K
Change in Entropy When Mixing Water at Different Temperatures
  • · Replies 5 ·
Replies
5
Views
2K
What is the Relationship Between Entropy and Temperature?
  • · Replies 2 ·
Replies
2
Views
2K
Ice cube in water: entropy calculation (Calorimetry)
  • · Replies 6 ·
Replies
6
Views
2K
How to calculate the entropy for two sources
  • · Replies 5 ·
Replies
5
Views
2K
Entropy and the Helmholtz Free Energy of a Mass-Piston System
  • · Replies 8 ·
Replies
8
Views
2K
Entropy change for water in contact with a reservoir
  • · Replies 4 ·
Replies
4
Views
5K
Does a Well-Defined Entropy Exist for Non-Ideal Gases A and B?
  • · Replies 1 ·
Replies
1
Views
1K
Computing entropy change of ideal gas during heating
  • · Replies 8 ·
Replies
8
Views
3K
Find rate of temperature change using heat capacity, density and area
  • · Replies 4 ·
Replies
4
Views
2K