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Chapter 12: Problem 22

How are the absolute temperature and volume of a gas related, at constant pressure?

Short Answer

Expert verified
The absolute temperature and volume of a gas are directly proportional to each other at a constant pressure. As the temperature increases, the volume increases and vice versa.

Step by step solution

01

Understand Charles's Law

Charles's Law states that for a given quantity of gas at a constant pressure, the volume is directly proportional to the absolute temperature. In other words, as the temperature increases, so does the volume, and vice versa. \[ V \propto T \]
02

Present the Formula

The mathematical representation of Charles's Law implies that the volume divided by the temperature is a constant, assuming pressure is constant. Expressing this mathematically, we have \[ V = kT \], where \(k\) is a constant factor, \(V\) is the volume and \(T\) is the absolute temperature.
03

Explain the relationship

Hence, if the temperature of a gas is increased at constant pressure, its volume is also increased; therefore, a larger temperature, in Kelvin, means a greater volume. Similarly, if the temperature is decreased, the volume also decreases; this means that a smaller temperature indicates a lesser volume. This relationship is linear and any changes to the temperature will correspondingly impact the volume.

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