Question

If the mean kinetic energy of Helium is 5000 J at 400 K, then the kinetic energy of neon at 800 K is

• A. 10000 J
• B. 12500 J
• C. 5000 J
• D. 20000 J

Hint:

For gases, the kinetic energy is directly proportional to the temperature. Doubling the temperature doubles the kinetic energy.

Answer 1

The Correct Option is A

The kinetic energy of a gas is directly proportional to the temperature for an ideal gas. The relationship between kinetic energy and temperature is given by: \[ \text{Kinetic Energy} \propto T \] This means that if the kinetic energy of helium is 5000 J at 400 K, the kinetic energy of neon at 800 K can be calculated by using the ratio of temperatures, assuming both gases behave ideally: \[ \frac{KE_{\text{Neon}}}{KE_{\text{Helium}}} = \frac{T_{\text{Neon}}}{T_{\text{Helium}}} \] Substituting the given values: \[ \frac{KE_{\text{Neon}}}{5000} = \frac{800}{400} = 2 \] Thus, the kinetic energy of neon at 800 K is: \[ KE_{\text{Neon}} = 5000 \times 2 = 10000 \text{ J} \] So, the correct answer is 10000 J.