 #1
 24
 4
Homework Statement:
 See attached
Homework Equations:

P*V / T= constant
P*V^(y) = constant (if process is adiabatic)
I'm not sure that this is an adiabatic process. As far as i can read, it is adiabatic if no HEAT or ENERGY is added. But pumping in molecules that are a nonzero temperature is an addition of energy, no?
Anyway  my solution with the assumption of an adiabatic process.
(skipping units for brevity):
P0 = 14.7
P1 = 50.0
T0 = 293
y = 1.40
We have:
P0 * V0^y = P1 *V1^y
So:
V1 / V0 = (P0 / P1)^(1/y)
And
P0*V0 / T0 = P1*V1 / T1
So:
P1 / P0 * V1 / V0 = T1 / T0
Inserting:
(P0 / P1)^(1) * (P0 / P1)^(1/y) = T1 / T0
T1 = (P0 / P1)^(1/y  1) * T0
Inserting the values we get
T1 = 415.7 K = 142.55 C
The answer in the book says 173 C.
Are my assumptions about adiabatic wrong? Or am i using the wrong equations?
Can i really use P*V / T = constant if we are adding air molecules with the pump?
Any suggestions would be appreciated.
Anyway  my solution with the assumption of an adiabatic process.
(skipping units for brevity):
P0 = 14.7
P1 = 50.0
T0 = 293
y = 1.40
We have:
P0 * V0^y = P1 *V1^y
So:
V1 / V0 = (P0 / P1)^(1/y)
And
P0*V0 / T0 = P1*V1 / T1
So:
P1 / P0 * V1 / V0 = T1 / T0
Inserting:
(P0 / P1)^(1) * (P0 / P1)^(1/y) = T1 / T0
T1 = (P0 / P1)^(1/y  1) * T0
Inserting the values we get
T1 = 415.7 K = 142.55 C
The answer in the book says 173 C.
Are my assumptions about adiabatic wrong? Or am i using the wrong equations?
Can i really use P*V / T = constant if we are adding air molecules with the pump?
Any suggestions would be appreciated.
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