Maxwell velocity distribution. Consider an ideal gas that obeys a Maxwell velocity distribution. Each particle has mass m. (a) Calculate the expected kinetic energy of a gas molecule using the Maxwell distribution. Could you have calculated the expected value another way? (b) Is your answer to part (a) equal to (i) mč² , (i) mužms , (i) mup, none of these. Recall C is the average speed,Urms is the root-mean-square speed, and Ump is the most probable speed. Show your work. (c) If the temperature is held constant, but the mass m of each particle is increased by a factor of 4, by how much does your answer to (a) change? By how much does C change?

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Maxwell velocity distribution. Consider an ideal gas that obeys a Maxwell velocity distribution.
Each particle has mass m.
(a) Calculate the expected kinetic energy of a gas molecule using the Maxwell distribution.
Could you have calculated the expected value another way?
(b) Is your answer to part (a) equal to (i)mc² , (ii)mums , (ii) ;mup, none of these.
Recall C is the average speed,Urms is the root-mean-square speed, and Ump is the most
probable speed. Show your work.
(c) If the temperature is held constant, but the mass m of each particle is increased by
a factor of 4, by how much does your answer to (a) change? By how much does C
change?
Transcribed Image Text:Maxwell velocity distribution. Consider an ideal gas that obeys a Maxwell velocity distribution. Each particle has mass m. (a) Calculate the expected kinetic energy of a gas molecule using the Maxwell distribution. Could you have calculated the expected value another way? (b) Is your answer to part (a) equal to (i)mc² , (ii)mums , (ii) ;mup, none of these. Recall C is the average speed,Urms is the root-mean-square speed, and Ump is the most probable speed. Show your work. (c) If the temperature is held constant, but the mass m of each particle is increased by a factor of 4, by how much does your answer to (a) change? By how much does C change?
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