- #1
Bill Foster
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Homework Statement
By means of a hand pump, you inflate a tire from 0 psi to 35 psi (overpressure). The volume of the tire remains constant at [tex]3.5 ft^3[/tex]. How much work must you do on the air pump? Assume each stroke of the pump is an adiabatic process and that the air is initially at STP.
Homework Equations
[tex]pV^\gamma=constant[/tex]
[tex]dW=pdV[/tex]
[tex]\Delta{Q}=nC_v\Delta{T}[/tex]
[tex]pV=nRT[/tex]
The Attempt at a Solution
I can't use [tex]dW=pdV[/tex] because the change in volume is 0.
[tex]p_0V^\gamma=p_1V^\gamma[/tex]
Since V is constant, that implies [tex]p_0=p_1[/tex]
So I'm left with [tex]\Delta{Q}=nC_v\Delta{T}[/tex] and [tex]pV=nRT[/tex]
Combining them, I get [tex]\Delta{Q}=\frac{C_v\Delta{p}V}{R}[/tex]
The problem is I don't know what [tex]C_v[/tex] is.
Since the value isn't given in my book, I assume that I'm suppose to calculate it.
I know that [tex]C_p=\frac{5}{2}R[/tex] for monotomic gas and [tex]C_p=\frac{7}{2}R[/tex] for diatomic. I assume air is a mixture of both.
But when I plug in the numbers (R=8.314) it just doesn't come out correctly.
The correct answer is [tex]8.1\times{10^3} ft\cdot{lb}=10982 J[/tex]. Working backwards from that answer I can see that [tex]C_v=3.82[/tex].
So what am I missing?