- #1
Zomboy
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Question:
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...
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...