Question

An automobile tire is filled to an absolute pressure of 3.0 atm at a temperature of $30^{\circ} \mathrm{C}$. Later it is driven to a place where the temperature is only $-20^{\circ} \mathrm{C} .$ What is the absolute pressure of the tire at the cold place? (Assume that the air in the tire behaves as an ideal gas and the volume is constant.)

Name: Problem 27, Chapter 10: College Physics
Uploaded: 2021-05-08T13:10:24-08:00
Duration: 1 min 18 s
Channel: Ajay Singhal
Description: An automobile tire is filled to an absolute pressure of 3.0 atm at a temperature of 30^∘ C. Later it is driven to a place where the temperature is only -20^∘ C . What is the absolute pressure of the tire at the cold place? (Assume that the air in the tire behaves as an ideal gas and the volume is constant.)

    An automobile tire is filled to an absolute pressure of 3.0 atm at a temperature of $30^{\circ} \mathrm{C}$. Later it is driven to a place where the temperature is only $-20^{\circ} \mathrm{C} .$ What is the absolute pressure of the tire at the cold place? (Assume that the air in the tire behaves as an ideal gas and the volume is constant.)

College Physics

Jerry D. Wilson,… 7th Edition

Chapter 10, Problem 27

Instant Answer

Solved by Expert Ajay Singhal

05/08/2021

Step 1

0 atm and the initial temperature $T_1$ is $30^{\circ} \mathrm{C}$ which is equal to $30 + 273 = 303$ K. The final temperature $T_2$ is $-20^{\circ} \mathrm{C}$ which is equal to $-20 + 273 = 253$ K. We are asked to find the final pressure $P_2$. Show more…

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An automobile tire is filled to an absolute pressure of 3.0 atm at a temperature of $30^{\circ} \mathrm{C}$. Later it is driven to a place where the temperature is only $-20^{\circ} \mathrm{C} .$ What is the absolute pressure of the tire at the cold place? (Assume that the air in the tire behaves as an ideal gas and the volume is constant.)

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Key Concepts

Temperature Conversion to Kelvin

In gas law calculations, temperatures must be in an absolute scale. Converting Celsius to Kelvin is essential since the Kelvin scale starts at absolute zero, ensuring that temperature ratios are valid in calculations.

Constant Volume Process

When the volume of a gas is held constant, the pressure becomes directly proportional to its absolute temperature. This relationship, derived from the ideal gas law, allows for determining the final pressure of a gas when there is a change in temperature.

Ideal Gas Law

This law provides the fundamental relationship for gases, expressed as PV = nRT, which connects pressure, volume, temperature, and the number of moles. It serves as the basis for understanding how changes in temperature affect pressure when volume and the amount of gas remain constant.

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