Question: The RMS speed of a gas is 250 m/s. What is the kinetic energy per molecule of the gas?
Options:
0.5 * m * (250)^2
0.25 * m * (250)^2
0.75 * m * (250)^2
1.5 * m * (250)^2
Correct Answer: 0.5 * m * (250)^2
Solution:
The kinetic energy per molecule is given by KE = (1/2) * m * v^2. Thus, KE = 0.5 * m * (250)^2.
The RMS speed of a gas is 250 m/s. What is the kinetic energy per molecule of th
Practice Questions
Q1
The RMS speed of a gas is 250 m/s. What is the kinetic energy per molecule of the gas?
0.5 * m * (250)^2
0.25 * m * (250)^2
0.75 * m * (250)^2
1.5 * m * (250)^2
Questions & Step-by-Step Solutions
The RMS speed of a gas is 250 m/s. What is the kinetic energy per molecule of the gas?
Step 1: Understand the formula for kinetic energy per molecule, which is KE = (1/2) * m * v^2.
Step 2: Identify the given values. The RMS speed (v) is 250 m/s.
Step 3: Note that we need the mass (m) of one molecule of the gas to calculate the kinetic energy.
Step 4: If the mass of one molecule is known, substitute the values into the formula: KE = 0.5 * m * (250)^2.
Step 5: Calculate (250)^2, which equals 62500.
Step 6: Multiply 0.5 by the mass (m) and then by 62500 to find the kinetic energy per molecule.
Kinetic Energy – The kinetic energy of an object is the energy it possesses due to its motion, calculated using the formula KE = (1/2) * m * v^2, where m is mass and v is velocity.
Root Mean Square Speed – RMS speed is a statistical measure of the speed of particles in a gas, which can be used to derive kinetic energy per molecule.
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