How do I calculate the gauge pressure?

In summary, the conversation discusses how to calculate the gauge pressure of an automobile tire after it has been running on a hot day. Using the equation ## \frac{P_1}{T_1} = \frac{P_2}{T_2} ## and assuming fixed volume and atmospheric pressure, the correct answer is approximately 2.5×10^5Pa, which is closest to option B. Answer A is incorrect and the problem may have a mistake.
  • #1
eprparadox
138
2

Homework Statement



An automobile tire is pumped up to a gauge pressure of ##2.0 \times 10^5 ## Pa when the temperature is 27◦ C. What is its gauge pressure after the car has been running on a hot day so that the tire temperature is 77◦ C? Assume that the volume remains fixed and take atmospheric pressure to be ##1.013 \times 10^5 ## Pa.

A. 1.6×10^5Pa
B. 2.6×10^5Pa
C. 3.6×10^5Pa
D. 5.9×10^5Pa
E. 7.9×10^5Pa

Homework Equations



## \frac{P_1}{T_1} = \frac{P_2}{T_2} ##

The Attempt at a Solution



I think you have to use absolute pressure and not gauge pressure so using the above equation, I got

[tex] \frac{2.0 \times 10^5 + 1.013 \times 10^5}{ 27 + 273} = \frac{x + 1.013 \times 10^5}{77 + 273} [/tex]

Solving for ## x ##, I get ##2.5 \times 10^5 Pa ##.

The answer given is A but I get closest to B.

Any thoughts on where I'm going wrong?
 
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  • #2
I agree with your answer. B appears to be the best answer.

EDIT: Answer A doesn't make sense if the tire is heated. I think you would get answer A if you assumed that the initial given pressure corresponds to 77o and then the tire is cooled to 27o. But that's not what the problem says.
 
Last edited:
  • #3
Yes. I also confirm your answer. A is just wrong. And B is a little too high, but acceptable.
 

Related to How do I calculate the gauge pressure?

1. How do I calculate gauge pressure?

To calculate gauge pressure, you need to subtract the atmospheric pressure from the absolute pressure. The formula for gauge pressure is: P gauge = P absolute - P atmospheric. You can measure atmospheric pressure using a barometer or find the average value for your location.

2. What is the difference between gauge pressure and absolute pressure?

Gauge pressure is measured relative to atmospheric pressure, while absolute pressure is measured relative to a perfect vacuum. This means that absolute pressure will always be higher than gauge pressure, as it includes the pressure of the atmosphere on top of the measured pressure.

3. What are the units for gauge pressure?

Gauge pressure is typically measured in units of pounds per square inch (psi) or kilopascals (kPa). Other units such as atmospheres (atm) or millimeters of mercury (mmHg) may also be used, depending on the context.

4. Can I convert gauge pressure to absolute pressure?

Yes, you can convert gauge pressure to absolute pressure by adding the atmospheric pressure to the gauge pressure. Keep in mind that the atmospheric pressure may vary depending on your location and environmental conditions.

5. How can I use gauge pressure in practical applications?

Gauge pressure is used to measure the pressure in closed systems such as pipes, containers, and tanks. It is essential in industries such as manufacturing, transportation, and engineering, where precise pressure measurements are necessary for safety and efficiency.

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