Adiabatic vs. Isothermal Expansion: How to Calculate Work and Temperature?

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SUMMARY

The discussion focuses on calculating work and temperature changes during adiabatic and isothermal expansions of an ideal monatomic gas. The problem involves four moles of gas expanding from an initial volume of 1 m³ at 300 K to a final volume of 10 m³. Key equations include the work done by the gas during adiabatic expansion, given by W = 1/(1-γ) × (PfVf - PiVi), and the relationship between pressure and volume in adiabatic processes, which is governed by the specific heat ratio (γ). The initial pressure can be determined using the ideal gas law, allowing for the calculation of final temperature and work done.

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  • Understanding of ideal gas laws and equations
  • Knowledge of adiabatic and isothermal processes
  • Familiarity with the specific heat ratio (γ) for monatomic gases
  • Basic thermodynamic principles related to work and energy
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  • Calculate the initial pressure using the ideal gas law: P = nRT/V
  • Explore the relationship between pressure and volume in adiabatic processes
  • Learn how to derive final temperature (Tf) from known variables in adiabatic expansion
  • Investigate the concept of energy transfer in isothermal processes and its implications
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Students studying thermodynamics, physics enthusiasts, and anyone seeking to understand the principles of gas expansion and work calculations in thermodynamic systems.

bio87
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Hi people!
So i have a homework question that i am stuck on!

Four moles of an ideal monatomic gas undergoes an adiabatic expansion from intial volume of 1m cubed and a temperature of 300k to a final volume of 10m cubed. a) How much wrk is done by the gas ? b) what is the final temperature? c) If instead the gas expands isothermally to 10m cubed, how much work is done? d) In part C where does the energy come from to perform the work? ...thats a lot!

I thought of using the equation of work W(by)= 1/(1-gamma) x (PfVf-PiVi) to fnd the answer for a...but I don't have the pressure..:rolleyes: then i thought that maybe I could use deltaE= Q(in) - W (by)...but I don't know the change in temperature, therefore; I am all over the place and I don't know where to start.. any hints/help would be appreciated! Thanks
 
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With the information you were given, you can find the initial pressure of the gas.
 
bio87 said:
I thought of using the equation of work W(by)= 1/(1-gamma) x (PfVf-PiVi) to fnd the answer for a...but I don't have the pressure..:rolleyes:
First work out the initial pressure, which is easy since you are given n,Ti and Vi.
What is the relationship between P and V in an adiabatic expansion/compression? (hint: it involves [itex]\gamma[/itex]). That will give you the final pressure and, if you know n, Vf and Pf you can determine Tf.

AM
 

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