Question

A group of 25 particles have the following speeds:

Answer 1

Answer:

Part a: The average speed is 24.12 m/s

Part b: The rms speed is 25.55 m/s

Part c: The most probable speed is 17 m/s.

Explanation:

Part a

Average Speed

Average speed is given as

$v_{avg}=\frac{\sum}{n}$

$v_{avg}=\frac{(2 \times 11) +(7 \times 17)+(4 \times 19)+(3 \times 27) +(6 \times 32) +(1 \times 33)+(2 \times 40) }{25}\\v_{avg}=\frac{22+119+76+81+192+33+80}{25}\\v_{avg}=\frac{603}{25}\\v_{avg}=24.12 m/s$

So the average speed is 24.12 m/s

Part b

RMS Speed

$v_{rms}=\frac{\sum v^2}{n}$

$v_{rms}=\sqrt{\frac{(2 \times 11^2) +(7 \times 17^2)+(4 \times 19^2)+(3 \times 27^2) +(6 \times 32^2) +(1 \times 33^2)+(2 \times 40^2) }{25}} \\v_{rms}=\sqrt{\frac{242+2023+1444+2187+6144+1089+3200}{25}}\\\\v_{rms}=\sqrt{\frac{16329}{25}}\\v_{rms}=\sqrt{653.16}\\v_{rms}=25.55 m/s$

So the rms speed is 25.55 m/s

Part c

Most Probable Speed

As 7 particles have speed of 17 m/s i.e. 7 is the highest frequency so 17 m/s is the most probable speed.