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The tire on a bicycle is filled with air to a gauge pressure of 744 kPa at 20◦C. What is the gauge pressure in the tire after a ride on a hot day when the tire air temperature is 65◦C? (Assume constant volume and a constant atmospheric pressure of 101.3 kPa.) Answer in units of kPa.

Respuesta :

Answer:[tex]P_f\left ( gauge\right )=975.124-101.3=873.824 KPa[/tex]

Explanation:

Given

[tex]P_i=744 KPa[/tex]

Initial Absolute pressure=744+101.3=845.3KPa

[tex]T_i=20 ^{\circ}C\approx 293 k[/tex]

[tex]T_f=65^{\circ}C\approx 338 k[/tex]

Using ideal gas equation

PV=mRT

here P=absolute pressure

Temperature in kelvin

thus [tex]\frac{845.3}{293}=\frac{P_f}{338}[/tex]

[tex]P_f=975.124KPa\left ( absolute\right )[/tex]

[tex]P_f\left ( gauge\right )=975.124-101.3=873.824 KPa[/tex]

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