A gas occupies a volume $V$ - AQA - A-Level Physics - Question 8 - 2021 - Paper 2

To find the new root mean square speed of the gas after compression, we can use the equation for the root mean square speed, which is given by:

c_{rms} = ext{constant} imes rac{T}{V}

Where:

• The root mean square speed is proportional to the square root of temperature and inversely proportional to the square root of volume.

Since the gas is compressed to a volume of $0.5V$ at constant temperature, we can set up the ratio:

c_{rms_{new}} = c_{rms_{initial}} imes rac{V^{1/2}}{(0.5V)^{1/2}}

Substituting the expressions: c_{rms_{new}} = u imes rac{V^{1/2}}{(0.5)^{1/2} V^{1/2}} = u imes rac{1}{(0.5)^{1/2}} = u imes rac{1}{rac{1}{rac{1}{2}}^{1/2}} = u imes 2 = 2u

Thus, the root mean square speed of the gas particles after compression is: $2u.$