Thermodynamics Work from pressure

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SUMMARY

The discussion focuses on calculating the work done during the isothermal compression of air in bicycle tires, specifically when the air pressure is increased to 80 psig. The relevant equation used is W = nRT * ln(V2/V1), where the volume of air is reduced by a factor of 5.7. The standard atmospheric pressure of 14.7 psi is added to the tire pressure to obtain a total pressure of 94.7 psi. The solution emphasizes that for calculating work per pound mass, the value of n is not necessary.

PREREQUISITES
  • Understanding of isothermal processes in thermodynamics
  • Familiarity with the ideal gas law (Pv = nRT)
  • Knowledge of logarithmic functions and their application in thermodynamic equations
  • Basic concepts of pressure measurement (psig and psi)
NEXT STEPS
  • Study the derivation and application of the ideal gas law in thermodynamic calculations
  • Learn about isothermal compression and its implications in real-world applications
  • Explore the concept of work done in thermodynamic systems, focusing on different processes
  • Investigate the significance of pressure ratios in gas compression scenarios
USEFUL FOR

This discussion is beneficial for students studying thermodynamics, engineers involved in mechanical design, and anyone interested in understanding the principles of gas compression and work calculations in practical applications.

Logan McEntire
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Homework Statement


The tires on a bicycle require an air pressure of 80 psig. When isothermally pumped up the bicycle tires, the volume of the air (that was originally in the atmosphere) is reduced by a factor of 5.7. Please determine the work that must be done on each lbm of air that is pumped into the tires. Please report your answer in lbf-ft/lbm.
.

Homework Equations


W=nRT*ln(V2/V1)
Pv=nRT

The Attempt at a Solution


My attempt might be very wrong, but this is what i tried.
I simplified Pv=nRT to T=PV/nR
Plugged that into W=nRT*ln(V2/V1)
W=PV*ln(V2/V1)
I know the standard pressure (14.7psi) and the pressure inside the tire (80psig+14.7psi=94.7psi), but I don't know the volume of to plug in for the V.
 
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Use nRT, with T equal to room temperature.
 
What do I use for n?
 
For isothermal compression P1/P2 =V2/V2, instead of using volume, you can use pressure ratio
 
Logan McEntire said:
What do I use for n?
You are trying to get the work per pound mass. So you don't need to know n. You are solving for W/n.
 

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