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:
[tex]\frac{P_1}{T_1}=\frac{P_2}{T_2}[/tex]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:
[tex]\begin{gathered} P_2=\frac{P_1T_2}{T_1} \\ \\ P_2=\frac{40.7*317}{282.7} \\ \\ P_2=\frac{12901.9}{282.7} \\ \\ P_2=45.6\text{4 lb/in}^2 \end{gathered}[/tex]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