If the RMS speed of a gas is 300 m/s, what is the RMS speed of the same gas at double the temperature?
Practice Questions
1 question
Q1
If the RMS speed of a gas is 300 m/s, what is the RMS speed of the same gas at double the temperature?
300 m/s
600 m/s
300√2 m/s
600√2 m/s
The RMS speed is proportional to the square root of the temperature. If the temperature is doubled, the RMS speed increases by a factor of sqrt(2). Therefore, the new RMS speed will be 300 * sqrt(2), which is approximately 600 m/s.
Questions & Step-by-step Solutions
1 item
Q
Q: If the RMS speed of a gas is 300 m/s, what is the RMS speed of the same gas at double the temperature?
Solution: The RMS speed is proportional to the square root of the temperature. If the temperature is doubled, the RMS speed increases by a factor of sqrt(2). Therefore, the new RMS speed will be 300 * sqrt(2), which is approximately 600 m/s.
Steps: 7
Step 1: Understand that RMS speed (Root Mean Square speed) of a gas is related to its temperature.
Step 2: Know that if the temperature of the gas is doubled, the RMS speed changes according to the formula: new RMS speed = old RMS speed * sqrt(new temperature / old temperature).
Step 3: Since the temperature is doubled, we can say new temperature / old temperature = 2.
Step 4: Therefore, the new RMS speed = old RMS speed * sqrt(2).
Step 5: Substitute the old RMS speed (300 m/s) into the equation: new RMS speed = 300 * sqrt(2).
Step 6: Calculate sqrt(2), which is approximately 1.414.
Step 7: Multiply 300 by 1.414 to find the new RMS speed: 300 * 1.414 = approximately 424.2 m/s.
