One mole of neon, a monatomic gas, starts out at STP.

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SUMMARY

In this discussion, the process of heating one mole of neon, a monatomic ideal gas, is analyzed under specific conditions. Initially, the gas is heated at constant volume until its pressure triples, followed by further heating at constant pressure until its volume doubles. The relevant equations used include the ideal gas law (PV=nRT), heat transfer equations (Q=nc(T2-T1)), and specific heat capacities (Cp=5/2R, Cv=3/2R). The final calculations confirm that the heat added to the gas can be determined using the change in temperature and the appropriate heat capacity.

PREREQUISITES
  • Understanding of the ideal gas law (PV=nRT)
  • Knowledge of heat transfer equations (Q=nc(T2-T1))
  • Familiarity with specific heat capacities for monatomic gases (Cp and Cv)
  • Basic thermodynamics concepts related to constant volume and constant pressure processes
NEXT STEPS
  • Calculate heat transfer for different gases using their specific heat capacities
  • Explore the implications of the ideal gas law under varying conditions
  • Study the differences between isochoric and isobaric processes in thermodynamics
  • Investigate real gas behavior compared to ideal gas assumptions
USEFUL FOR

This discussion is beneficial for students studying thermodynamics, particularly those focusing on gas laws and heat transfer, as well as educators seeking to clarify concepts related to ideal gases and their behaviors under different thermal conditions.

GabrielleP
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Homework Statement



One mole of neon, a monatomic gas, starts out at STP. The gas is heated at constant volume until its pressure is tripled, then further heated at constant pressure until its volume is doubled. Assume that neon behaves as an ideal gas. For the entire process, find the heat added to the gas.

Homework Equations


Q=nc(T2-T1)
PV=nRT
Cp=5/2R
Cv=3/2R

The Attempt at a Solution


Cp=5/2(8.31)=20.775
Cv=3/2(8.31)=12.465
P=3Po=303900 Pa
V=2Vo=44.8*10^-3 m^3
Help?
 
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Ok, i figured out how to do it. Thanks anyways!
 


Welcome to PF GabrielleP! :smile:

GabrielleP said:

Homework Statement



One mole of neon, a monatomic gas, starts out at STP. The gas is heated at constant volume until its pressure is tripled, then further heated at constant pressure until its volume is doubled. Assume that neon behaves as an ideal gas. For the entire process, find the heat added to the gas.

Homework Equations


Q=nc(T2-T1)
PV=nRT
Cp=5/2R
Cv=3/2R

Be careful how you write these last two expressions. Right now it's ambiguous whether you mean (5/2)R or 5/(2R). (But of course, we know that it should be the former).

GabrielleP said:

The Attempt at a Solution


Cp=5/2(8.31)=20.775
Cv=3/2(8.31)=12.465
P=3Po=303900 Pa
V=2Vo=44.8*10^-3 m^3
Help?

Yes, good. Start with the ideal gas law:

PV = nRT

If V is constant, then we can write

P = (nR/V)*T = (const)*T

in other words, at constant volume, the pressure is just proportional to the temperature (or in other words, the pressure scales linearly with the temperature). This means that if I triple the pressure, I must have tripled the temperature. To illustrate that, start at P0:

P0 = (nR/V)T0

Now if the pressure was tripled, then we now have:

P = (nR/V)*T = 3P0 = 3(nR/V)*T0

So we conclude that the new temperature T = 3T0.

Since you know the change in temperature (T - T0 = 2T0), you can figure out how much heat must have been added to the system using the heat capacity at constant volume, and the appropriate equation.

You would use a similar approach for solving the second part: start with the ideal gas law, and see what happens at constant pressure.
 

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