Table of contents

21. Kinetic Theory of Ideal Gases

The Ideal Gas Law

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Multiple Choice

An ideal gas is in a sealed container. It has a temperature T when it has volume V at pressure P. What is the temperature of the gas when its volume is quadrupled, and the pressure is halved?

T/8

T/4

T/2

Verified step by step guidance

Start by recalling the ideal gas law, which is given by the equation:

P V = n R T

, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

Since the number of moles n and the gas constant R remain constant, we can use the relationship:

\frac{P}{T} = \frac{P'}{T'}

, where P' and T' are the new pressure and temperature, respectively.

Substitute the given changes into the equation: the volume is quadrupled (V' = 4V) and the pressure is halved (P' = P/2).

Using the ideal gas law, set up the equation for the initial and final states:

\frac{P}{T} = \frac{\frac{P}{2}}{T'}

Solve for the new temperature T' by rearranging the equation:

T' = 2 T

. This shows that the new temperature is twice the original temperature.

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