How to Determine the Temperature of Balloon Y with Two Helium Balloons?

Question:

If balloon X is at 300 K and the rate of effusion in balloon Y is twice that of balloon X, what is the temperature of balloon Y?

Answer:

The temperature of balloon Y can be determined using Graham's law of effusion, which relates effusion rate to temperature. If balloon X is at 300 K and balloon Y has twice the effusion rate, the temperature of balloon Y is 1200 K.

Explanation:

When dealing with two balloons filled with helium gas, it is important to consider the rate of effusion and how it correlates with temperature. In this scenario, with balloon X at 300 K, and balloon Y effusing at twice the rate of balloon X, we can apply Graham's law.

Graham's law of effusion states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Additionally, the kinetic theory of gases tells us that the average kinetic energy of gas particles is directly proportional to the temperature in kelvins.

Since the rate of effusion is directly related to the square root of temperature, if balloon Y is effusing at twice the rate of balloon X, its temperature should be four times that of balloon X. Therefore, the temperature of balloon Y is 1200 K.

By understanding these principles and applying Graham's law, we can determine the temperature of balloon Y accurately. It is important to grasp the concepts of effusion rate and temperature to make such calculations.