If the RMS speed of a gas is 300 m/s at 400 K, what will be the RMS speed at 200 K?
Practice Questions
1 question
Q1
If the RMS speed of a gas is 300 m/s at 400 K, what will be the RMS speed at 200 K?
150 m/s
300 m/s
600 m/s
100 m/s
The RMS speed is proportional to the square root of the temperature. Therefore, at 200 K, the RMS speed will be 300 * sqrt(200/400) = 150 m/s.
Questions & Step-by-step Solutions
1 item
Q
Q: If the RMS speed of a gas is 300 m/s at 400 K, what will be the RMS speed at 200 K?
Solution: The RMS speed is proportional to the square root of the temperature. Therefore, at 200 K, the RMS speed will be 300 * sqrt(200/400) = 150 m/s.
Steps: 10
Step 1: Understand that RMS speed is related to temperature. It is proportional to the square root of the temperature.
Step 2: Write down the formula for RMS speed: v_rms ∝ √T, where v_rms is the RMS speed and T is the temperature in Kelvin.
Step 3: Identify the initial conditions: RMS speed (v_rms1) = 300 m/s at temperature (T1) = 400 K.
Step 4: Identify the new temperature: T2 = 200 K.
Step 5: Set up the ratio using the proportionality: v_rms2 / v_rms1 = √(T2 / T1).
Step 6: Substitute the known values into the equation: v_rms2 / 300 = √(200 / 400).
