Question

What would be the gauge pressure in the tire when it’s temperature rises to 44 degrees Celsius

Answer 1

Question 007.

Given:

• Temperature, T1 = 9.7° C

,

• Pressure, P1 = 26 lb/in²

,

• New temperature, T2 = 44° C

,

• Atmospheric pressure = 14.7 lb/in²

Let's find the gauge pressure in the tire when the temperature rises.

To find the gauge pressure, apply the formula:

`(P_1)/(T_1)=(P_2)/(T_2)`

Where:

P2 is the new pressure.

P1 = 26 lb/in² + 14.7 lb/in² = 40.7 lb/in²

T1 is the initial temperature in kelvin = 9.7 + 273 = 282.7 K

T2 is the final temperature in kelvin = 44 + 273 = 317 K

Rewrite the formula for P2, input the values and solve.

We have:

`\begin{gathered} P_2=(P_1T_2)/(T_1) \\ \\ P_2=(40.7*317)/(282.7) \\ \\ P_2=(12901.9)/(282.7) \\ \\ P_2=45.6\text{4 lb/in}^2 \end{gathered}`

Hence, the gauge pressure will be:

P2 = 45.64 lb/in² - 14.7 lb/in² = 30.94 lb/in²

Therefore, the gauge pressure in the tire when its temperature rises to 44° C is 30.94 lb/in².

ANSWER:

30.94 lb/in²