What is the relationship between RMS speed and kinetic energy of gas molecules?
Practice Questions
1 question
Q1
What is the relationship between RMS speed and kinetic energy of gas molecules?
Directly proportional
Inversely proportional
No relationship
Depends on the gas
The kinetic energy of gas molecules is directly proportional to the square of the RMS speed, as KE = (1/2)mv_rms^2.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the relationship between RMS speed and kinetic energy of gas molecules?
Solution: The kinetic energy of gas molecules is directly proportional to the square of the RMS speed, as KE = (1/2)mv_rms^2.
Steps: 5
Step 1: Understand that gas molecules are always moving and have kinetic energy due to their motion.
Step 2: Learn that RMS speed (Root Mean Square speed) is a way to measure the average speed of gas molecules.
Step 3: Know the formula for kinetic energy (KE) of an object, which is KE = (1/2)mv^2, where m is mass and v is speed.
Step 4: Replace v in the kinetic energy formula with v_rms (the RMS speed) to get KE = (1/2)m(v_rms)^2.
Step 5: Notice that the kinetic energy depends on the square of the RMS speed, meaning if the RMS speed increases, the kinetic energy increases even more.
