What is the Work Done by an Ideal Gas Expanding at Constant Temperature?

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SUMMARY

The work done by an ideal gas expanding at constant temperature can be calculated using the formula W=2.303nRTlog(v2/v1). In this scenario, with two moles of gas at a temperature of 400 K and a gas constant R of 8.32, the calculation yields a work value of 4613.959 J when using the logarithm base 10. However, the correct approach for this problem is to use the natural logarithm, leading to a work done of 554.6 J. This discrepancy highlights the importance of using the appropriate logarithmic function in thermodynamic calculations.

PREREQUISITES
  • Understanding of ideal gas laws
  • Familiarity with thermodynamic equations
  • Knowledge of logarithmic functions, specifically natural logarithm (ln) and common logarithm (log)
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation of the ideal gas law and its applications
  • Learn about the differences between natural logarithm (ln) and common logarithm (log)
  • Explore the concept of isothermal processes in thermodynamics
  • Practice calculating work done in various thermodynamic processes
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Students studying thermodynamics, physics enthusiasts, and anyone looking to understand the principles of work done by gases during expansion processes.

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Homework Statement



Two moles of an ideal gas expand to double the initial volume at a constant temperature of 400 K. Calculate the work done by the process.

Homework Equations



W=2.303nRTlog(v2/v1)

The Attempt at a Solution



i tried the formula and got 4613.959 J but the answer is 554.6 J
 
Last edited:
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Are you sure it isn't log(V2/V1)? I'm used to the form W=nRTln(V2/V1). I can't get either of those answers. Can you show how you got that?
 
hage567 said:
Are you sure it isn't log(V2/V1)? I'm used to the form W=nRTln(V2/V1). I can't get either of those answers. Can you show how you got that?

n=2; v2=2*v1;T=400 K; R=8.32

W=2.303nRTlog(v2/v1)
= 2.303*2*8.32*400*log(2v1/v1)
= 2.303*2*8.32*400*log(2)
= 2.303*2*8.32*400*0.3010
= 4613.959

we generally use logarithms and i don't know wat is "ln"
 

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