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Chapter 5: Problem 13

Air is allowed to escape from an inflated tire. Is the temperature of the escaping air higher than, lower than, or equal to the temperature of the air inside the tire? Why?

Short Answer

Expert verified
Answer: The temperature of the air escaping from an inflated tire is lower than the temperature inside the tire.

Step by step solution

01

Recall the Ideal Gas Law

The Ideal Gas Law is given by the equation: PV = nRT where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
02

Analyze pressure and temperature relationship

From the Ideal Gas Law, we know that when the pressure (P) decreases, the product of pressure and volume (PV) must decrease too, assuming n, R and V to be constant. If PV decreases, then nRT must also decrease, since all gas particles follow the same Ideal Gas Law.
03

Extract the effect on temperature

Since n and R are constants, if PV decreases, then T (temperature) must also decrease. So, when the pressure of the air inside the tire decreases as it escapes, the temperature of the escaping air must also decrease.
04

Compare the temperature of escaping air and air inside the tire

As we found in step 3, the temperature of the escaping air decreases when the pressure decreases. Therefore, the temperature of the escaping air is lower than the temperature of the air inside the tire.

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