b) A nearly flat bicycle tire becomes noticeably warmer after it has been pumped Approximate this process as a reversible adiabatic compression. Take the initial pres and initial temperature of the air before it is put in the tire to be P = 1.00 bar and T = K. The final volume of the air in the tire is V = 1.00 L and the final pressure is P = bar.

Elements Of Electromagnetics
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b) A nearly flat bicycle tire becomes noticeably warmer after it has been pumped up.
Approximate this process as a reversible adiabatic compression. Take the initial pressure
and initial temperature of the air before it is put in the tire to be P = 1.00 bar and T; = 298
K. The final volume of the air in the tire is V = 1.00 L and the final pressure is Pf = 5.00
bar.
Hints:
• Cy.m = 5/2 R.
Heat Capacity ratio, y =
Cp.m
Cy,m
= 1.4
%3D
Cy,m
For a reversible adiabatic change, 4 = (4 )°, where c =
R
For perfect gas: CP.m - Cv,m = R
CP.m and Cv.m denote molar heat capacity at constant pressure and volume,
respectively. Tand V are temperature and volume at initiate (i) state ad final (f) state.
i) Derive a mathematical expression to show the relationship of temperature, volume
and heat capacity ratio (y) for the transformation of this process from initial to final
states.
Transcribed Image Text:b) A nearly flat bicycle tire becomes noticeably warmer after it has been pumped up. Approximate this process as a reversible adiabatic compression. Take the initial pressure and initial temperature of the air before it is put in the tire to be P = 1.00 bar and T; = 298 K. The final volume of the air in the tire is V = 1.00 L and the final pressure is Pf = 5.00 bar. Hints: • Cy.m = 5/2 R. Heat Capacity ratio, y = Cp.m Cy,m = 1.4 %3D Cy,m For a reversible adiabatic change, 4 = (4 )°, where c = R For perfect gas: CP.m - Cv,m = R CP.m and Cv.m denote molar heat capacity at constant pressure and volume, respectively. Tand V are temperature and volume at initiate (i) state ad final (f) state. i) Derive a mathematical expression to show the relationship of temperature, volume and heat capacity ratio (y) for the transformation of this process from initial to final states.
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