If the RMS speed of a gas is 300 m/s, what is the RMS speed of the same gas at d
Practice Questions
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
Questions & Step-by-Step Solutions
If the RMS speed of a gas is 300 m/s, what is the RMS speed of the same gas at double the temperature?
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.
RMS Speed and Temperature Relationship – The root mean square (RMS) speed of a gas is directly proportional to the square root of its absolute temperature, as described by the equation v_rms = sqrt(3kT/m), where k is the Boltzmann constant, T is the temperature, and m is the mass of the gas particles.
