Thermodynamics Question and My Answer

[Altairs]

[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 $$77^oF$$ and volume of the tire is $$1ft^3$$. Later, the sun comes out and the air inside the tire experience a temperature rise of $$36^oF$$. 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 $$\frac{lbf}{ft^2}$$

The Attempt at a Solution

First did the relevant conversions.

Then used :-

$$P_{1}v = RT_{1}$$

$$P_{2}v = RT_{2}$$

Where $$R$$ = Individual Gas Constant

Where $$v$$ = Specific Volume

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

$$\frac{P_{1}}{P_{2}} = \frac{T_{1}}{T_{2}}$$

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 ?

 

[Mapes]

Yes.