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Altairs

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**[SOLVED] Thermodynamics Question and My Answer**

## Homework Statement

During a cloudy day of the summer season, a driver inflates his car tyres (max allowed pressure is 44PSI(Gauge)) to 38PSI(Gauge) at a petrol station. the temperature of the air inside one of the tires is [tex]77^oF[/tex] and volume of the tire is [tex]1ft^3[/tex]. Later, the sun comes out and the air inside the tire experience a temperature rise of [tex]36^oF[/tex]. Assuming the volume to be constant determine whether the tire will burst or not.

## Homework Equations

P(Absolute) = P(Ambient) + P (Gauge)

Conversion from F to R

Conversion from PSI to [tex]\frac{lbf}{ft^2}[/tex]

## The Attempt at a Solution

First did the relevant conversions.

Then used :-

[tex]P_{1}v = RT_{1}[/tex]

[tex]P_{2}v = RT_{2}[/tex]

Where [tex]R[/tex] = Individual Gas Constant

Where [tex]v[/tex] = Specific Volume

Took the ratios, because the volume remains constant and so does the value of R :-

[tex] \frac{P_{1}}{P_{2}} = \frac{T_{1}}{T_{2}}[/tex]

Made relevant calculations and then did reverse conversions. Got the answer to be 41.54 PSI (Gauge). Which indicates that tire doesn't bursts. Is this the correct answer ?

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