If the average kinetic energy of the molecules of a monatomic ideal gas at 55°C is doubled,what is the resulting temperature of the gas?

Question

Quizplus · Accepted Answer

According to the kinetic theory of gases, the average kinetic energy of the molecules of a monatomic ideal gas is directly proportional to the temperature of the gas. Therefore, if the average kinetic energy is doubled, the temperature of the gas will also double. Using the formula:

Kinetic energy per molecule = 3/2 * k * T

Where k is the Boltzmann constant and T is the temperature in Kelvin. If we double the kinetic energy, it becomes:

2 * KE = 3/2 * k * 2T
2 * KE = 3 * k * T

Solving for T, we get:

T = (2 * KE) / (3 * k)

Using the given temperature of 55°C = 328K and doubling the kinetic energy, we get:

T = (2 * 3/2 * 1.38E-23 J/K * 328K) / (3 * 1.38E-23 J/K)
T = 2 * 328K
T = 656K

Converting back to Celsius, we get 383°C which is option D.

If the Average Kinetic Energy of the Molecules of a Monatomic