Finding the amount of heat required to double volume?

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SUMMARY

To determine the heat required to double the volume of 1.35 mol of oxygen (O2) starting at 11.0°C, the equation Q=nCpΔT is utilized, where Cp is given as 7R/2. The challenge lies in linking the change in volume to the heat equation, which can be approached using the ideal gas law and conservation of mass principles. The pressure (P) is not specified, indicating the need for further calculations to establish the relationship between heat, volume change, and temperature change.

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  • Understanding of the ideal gas law
  • Knowledge of molar specific heats (Cp and Cv)
  • Familiarity with thermodynamic equations
  • Basic algebra for solving simultaneous equations
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  • Learn about the conservation of mass in thermodynamic processes
  • Explore the relationship between pressure, volume, and temperature changes in gases
  • Investigate how to derive and use the equations for internal energy changes (ΔEint)
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Students in thermodynamics, physics enthusiasts, and anyone involved in gas laws and heat transfer calculations will benefit from this discussion.

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Homework Statement



In an experiment, 1.35 mol of oxygen (02) are heated at constant pressure starting at 11.0°C. How much heat must be added to the gas to double its volume? You may assume without proof, that the molar specific heats are cp=7R/2 and cv=5R/2.



Homework Equations





The Attempt at a Solution



My working so far...

Q=nCpΔT

Q=n(7R/2)ΔT

Q= 1.35(7R/2)(s-11) -----> where s= Tf

But I need some equation linking change in volume to this...

ie Q= -PΔV

But I don't Know what P is?

Perhaps I need something with ΔEint but I am not to sure.
I was thinking I will need to solve the first equation simultaneously with one with ΔV

I'm stuck as to where to go from here??

Please help any advice is greatly noted.
 
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Hint: Use the ideal gas law followed by a conservation of mass.
 

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