Ideal Gas Final Temperature and Heat Calculation

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SUMMARY

The discussion focuses on calculating the final temperature and heat added during the compression of 0.020 mol of a diatomic gas, initially at 20°C, compressed from 1500 cm³ to 500 cm³ under the condition that pV² remains constant. The final temperature was determined to be 606°C. The participant also calculated the constant value to be approximately 0.07304 and recognized that the relationship between pressure and volume allows for the calculation of work done on the gas, which can be used alongside the first law of thermodynamics to find the heat added.

PREREQUISITES
  • Understanding of the ideal gas law (PV=nRT)
  • Knowledge of thermodynamic processes and the first law of thermodynamics
  • Familiarity with the concept of work done on gases
  • Basic skills in algebra for manipulating equations
NEXT STEPS
  • Study the derivation and implications of the ideal gas law (PV=nRT)
  • Learn about different thermodynamic processes, specifically polytropic processes
  • Explore the first law of thermodynamics and its applications in heat transfer calculations
  • Investigate methods for calculating work done on gases in variable pressure-volume scenarios
USEFUL FOR

This discussion is beneficial for students studying thermodynamics, particularly those working on gas laws and heat transfer calculations, as well as educators seeking to clarify concepts related to polytropic processes and the first law of thermodynamics.

Eastonc2
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Homework Statement



0.020 mol of a diatomic gas, with initial temp. of 20 C, are compressed from 1500 cm^3 to 500 cm^3 in a process in which pV^2=const.

a.) What is the final temp. in C?

b.) how much heat is added during this process?

Homework Equations



PV=nRT

The Attempt at a Solution



I've determined the final temperature to be 606 C, but can't find or think of what type of thermodynamic process, if any, pV^2=const. applies to.

I calculated the const.=~.07304 by setting pV^2=x and solving for x, but I'm not sure if that is even useful, and if it is, how it would be.
 
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Since you know how P varies with V, you can calculate the work done on the gas. Given the info you already calculated, you can then use the first law to calculate the heat Q.
 
Thanks, I discovered that on my own, and felt like an idiot, on my own. I guess I was just thinking about the problem too much to realize that I already had a way to find p with relation to V.
 

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