An automobile tire is inflated with air originally at 10.0°C and normal atmospheric pressure. During the process, the air is compressed to 31.5% of its original volume and the temperature is increased to 35.5°C. (a) What is the tire pressure in pascals? (b) After the car is driven at high speed, the tire's air temperature rises to 85.0°C and the tire's interior volume increases by 2.00%. What is the new tire pressure (absolute) in pascals?

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Step 1
(a) The ideal-gas equation describes each condition of the air in the tire. We will set up ratios in order to describe these changes. Dividing the equations PV = nRT in the initial and final
states, we have
PfVf
Tf
P¡Vi Ti
Solving for the final pressure in the tire, gives
Pf
=
=
=
which gives
I
Tf
P(V)()
P₁
Vf
T₁
=
(1.013 x 105 Pa)
x 105 Pa.
Note that the volume V¡ cancels out of the equation.
=
Vf
Po = Pr (V ( ) ( )
Pd
Pf
Vi
V₁
Step 2
(b) After the car is driven, the temperature and volume of air in the tire have changed. Let Td be the temperature and Vd be the volume of air in the tire. We have
PdVd
Td
PfVf
Tf'
x 105 Pa
273 +
273 +
Vf
Vf
Again we see that the volume Vf cancels out of the equation.
°C
K
°℃
K
=
x 105 Pa.
Transcribed Image Text:Step 1 (a) The ideal-gas equation describes each condition of the air in the tire. We will set up ratios in order to describe these changes. Dividing the equations PV = nRT in the initial and final states, we have PfVf Tf P¡Vi Ti Solving for the final pressure in the tire, gives Pf = = = which gives I Tf P(V)() P₁ Vf T₁ = (1.013 x 105 Pa) x 105 Pa. Note that the volume V¡ cancels out of the equation. = Vf Po = Pr (V ( ) ( ) Pd Pf Vi V₁ Step 2 (b) After the car is driven, the temperature and volume of air in the tire have changed. Let Td be the temperature and Vd be the volume of air in the tire. We have PdVd Td PfVf Tf' x 105 Pa 273 + 273 + Vf Vf Again we see that the volume Vf cancels out of the equation. °C K °℃ K = x 105 Pa.
An automobile tire is inflated with air originally at 10.0°C and normal atmospheric pressure. During the process, the air is compressed to 31.5% of its original volume and the
temperature is increased to 35.5°C.
(a) What is the tire pressure in pascals?
(b) After the car is driven at high speed, the tire's air temperature rises to 85.0°C and the tire's interior volume increases by 2.00%. What is the new tire pressure (absolute) in
pascals?
Transcribed Image Text:An automobile tire is inflated with air originally at 10.0°C and normal atmospheric pressure. During the process, the air is compressed to 31.5% of its original volume and the temperature is increased to 35.5°C. (a) What is the tire pressure in pascals? (b) After the car is driven at high speed, the tire's air temperature rises to 85.0°C and the tire's interior volume increases by 2.00%. What is the new tire pressure (absolute) in pascals?
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