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An automobile tire having a temperature of −1.9◦C (a cold tire on a cold day) is filled to a gauge pressure of 21 lb/in^2.
What would be the gauge pressure in the
tire when its temperature rises to 27◦C? For
simplicity, assume that the volume of the tire
remains constant, that the air does not leak
out and that the atmospheric pressure remains constant at 14.7 lb/in^2.
Answer in units of lb/in^2.

Respuesta :

Answer:

Gauge pressure inside the tyre is given as

[tex]P = 23.2 lb/in^2[/tex]

Explanation:

As we know that the volume of the tyre is constant

so here we can use

[tex]PV = nRT[/tex]

so we will have

[tex]\frac{P_1}{T_1} = \frac{P_2}{T_2}[/tex]

so we have

[tex]P_1 = 21 lb/in^2[/tex]

[tex]T_1 = -1.9 = 271.1 k[/tex]

[tex]T_2 = 273 + 27 = 300 k[/tex]

now we have

[tex]\frac{21}{271.1} = \frac{P}{300}[/tex]

[tex]P = 23.2 lb/in^2[/tex]

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