Compressing ideal gas isothermally, calc work

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SUMMARY

In this discussion, the work done on 10 moles of an ideal gas during isothermal and reversible compression from 1 to 10 atmospheres at 300K is calculated using the equation W = ∫(P dV). The ideal gas law (PV = nRT) is utilized to determine the initial and final volumes, allowing for the integration of pressure over the volume change. The final result involves the natural logarithm, confirming the relationship between pressure and volume during the process.

PREREQUISITES
  • Understanding of the ideal gas law (PV = nRT)
  • Familiarity with thermodynamic concepts, specifically isothermal processes
  • Knowledge of calculus, particularly integration techniques
  • Ability to manipulate equations involving pressure and volume
NEXT STEPS
  • Learn how to derive the work done in isothermal processes for different gases
  • Study the Clapeyron equation in detail for various thermodynamic applications
  • Explore the use of TeX for formatting mathematical equations in discussions
  • Investigate the implications of reversible versus irreversible processes in thermodynamics
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Students studying thermodynamics, particularly those focusing on ideal gas behavior and isothermal processes, as well as educators looking for practical examples of work calculations in thermodynamic systems.

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Homework Statement



10 moles of an ideal gas are compressed isothermally and reversibly from 1 to 10 atmospheres at 300K. Determine the work done ON the gas.

Homework Equations



dw=-PdV
PV=nRT

The Attempt at a Solution



dT=0
T=300K
dP=10atm

calc dV from ideal gas law = 2.27e10 m^3

so now we have dV for work eqn, but P is not constant?

Thanks.
 
Last edited:
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As much as I don't like thermodynamics, it doesn't seem very complicated.
Start with claperyon equation nr. 1:
p1V1=nRT
which allows you to calculate the first volume.
Equation nr.2:
p2V2=nRT
allows you to calculate 2nd volume. Hence you've got your integrating limits.
Now, I wish I knew how to use TeX in here :/.
Anyway,
<br /> W=\int\limits_{v_1}^{v_2} pdV
As you mentioned, p is not constant, but you can, again, calculate it easily from clapeyron's equation:
pV=nRT. And then substitute p under integral with what you've got, integrate. Should get natural logarithm.
 
Last edited:
Thank you, irycio!
 

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