Ratio of Number of Molecules in Two Vessels – Rankers Physics

Kinetic Theory of Gases: Practice Problem & Solution

A vessel contains gas A at pressure \(P\), volume \(V\) and temperature \(T\). Another vessel contains gas B at pressure \(2P\), volume \(\frac{V}{2}\) and temperature \(2T\). Ratio of number of molecules of B to A will be
\(\frac{1}{2}\)
2
4
\(\frac{1}{4}\)

Solution Explained:

To solve this problem, we apply the core principles of Kinetic Theory of Gases. Understanding the underlying formula is key to arriving at the correct answer below:

From the ideal gas law, \(PV = N k_B T\) which gives \(N = \frac{PV}{k_B T}\). Taking the ratio: \(\frac{N_B}{N_A} = \frac{P_B V_B / T_B}{P_A V_A / T_A} = \frac{2P times (V/2) / 2T}{PV / T} = \frac{1}{2}\).

Leave a Reply

Your email address will not be published. Required fields are marked *

Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. The percentage change in length of 1 m iron rod if its temperature changes by 100ºC is (\(\alpha\) for iron is \(2 \times 10^{-5}/\text{ºC}\))
2. Radiation energy corresponding to the temperature $T$ of the sun is $E$. If its temperature is doubled, then its radiation energy will be: (1990)
3. Assertion (A): It is not possible for a system, unaided by an external agency to transfer heat from a body at lower temperature to another body a higher temperature. Reason (R): According to Clausius statement "No process is possible whose sole result is the transfer of heat from a cooled object to a hotter object".  
4. A body cools from a temperature $3T$ to $2T$ in $10$ minutes. The room temperature is $T$. Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next $10$ minutes will be: (2016 - II)
5. Assertion (A): Molar heat capacity of an ideal monoatomic gas at constant volume is a constant at all temperatures. Reason (R): As the temperature of an monoatomic ideal gas is increased, number of degrees of freedom of gas molecules remains constant.