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in a bicycle pump the preasure increases from [p1 = 10^5] to [p2 = 30^5]. If the process is adiabatic ant the air starts at [T1 = 293 K], find the maximum temperature of the air in the pump. (Assuming air can be treated as an ideal gas)

Attempt:

So using the 1st Law and given that its adiabatic (no heat input/output) I've written:

U = W

(C_v)dT = PdV

(C_v)dT = (nR) (1/v) dV

then integrated and re-arranged to obtain:

T2 / T1 = (V2/V1)^(nR/c)

then substituted in { C_v = nR5/2 } because its an adiabatic process, and { T2 P1 / P2 T1 } for V2/V1 using the equation for an ideal gas...

But then when I re-arranged to find T2 I found it to be 33K which is wrong of course...

Is this sort of the way to do it? Its just I can't think of another way seeing as it doesn't specify the initial volume of the tyre...

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# Homework Help: (THERMO) - Adiabatic Expansion - known P1, P2, and T1

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