The Maxwell speed distribution function is given by; 3/2 m f(v) = mv² 2kBT 2πkBT i) Show that the average speed of the molecule is given by; 8KBT πm Hint: Use the standard integral; with the standard results; Io I₁ 1₁ = ²8 20² = 2α I2n where n = N/V is the number density. iii) Use the ideal gas law to show that; Φ 4TU² exp r³ exp[-ar²] dr = = 2n 1 2α 21. -12n-2, I2n+1 = ii) Use the one-dimensional velocity distribution to show that the flux is given by; Þ= n(v), P √2лmkBT n -12n-1. α
The Maxwell speed distribution function is given by; 3/2 m f(v) = mv² 2kBT 2πkBT i) Show that the average speed of the molecule is given by; 8KBT πm Hint: Use the standard integral; with the standard results; Io I₁ 1₁ = ²8 20² = 2α I2n where n = N/V is the number density. iii) Use the ideal gas law to show that; Φ 4TU² exp r³ exp[-ar²] dr = = 2n 1 2α 21. -12n-2, I2n+1 = ii) Use the one-dimensional velocity distribution to show that the flux is given by; Þ= n(v), P √2лmkBT n -12n-1. α
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[THERMAL DYNAMICS]
![The Maxwell speed distribution function is given by;
3/2
m
f(v) =
mv²
2kBT
2πkBT
i) Show that the average speed of the molecule is given by;
8KBT
πm
Hint: Use the standard integral;
with the standard results;
Io
I₁
1₁ = ²8 20²
=
2α
I2n
where n = N/V is the number density.
iii) Use the ideal gas law to show that;
Φ
4TU² exp
r³ exp[-ar²] dr
=
=
2n 1
2α
21.
-12n-2, I2n+1 =
ii) Use the one-dimensional velocity distribution to show that the flux is given by;
Þ= n(v),
P
√2лmkBT
n
-12n-1.
α](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F19ffe726-82ee-48ef-b9cf-b3664871e894%2Fbdbb90bd-8539-42db-a78e-b353a6ba178b%2Fbqu5h2j_processed.png&w=3840&q=75)
Transcribed Image Text:The Maxwell speed distribution function is given by;
3/2
m
f(v) =
mv²
2kBT
2πkBT
i) Show that the average speed of the molecule is given by;
8KBT
πm
Hint: Use the standard integral;
with the standard results;
Io
I₁
1₁ = ²8 20²
=
2α
I2n
where n = N/V is the number density.
iii) Use the ideal gas law to show that;
Φ
4TU² exp
r³ exp[-ar²] dr
=
=
2n 1
2α
21.
-12n-2, I2n+1 =
ii) Use the one-dimensional velocity distribution to show that the flux is given by;
Þ= n(v),
P
√2лmkBT
n
-12n-1.
α
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