The absolute temperature of an ideal diatomic gas is quadruple what happens to the average speed molecules
Answers
Answer:
The root-mean-square speed
u
rms
of gas particles is given by the equation
u
rms
=
√
3
R
T
M
M
where
R
is the universal gas constant, for this case
8.314
kg
⋅
m
2
s
2
⋅
mol
⋅
K
T
is the absolute temperature of the system, in
K
M
M
is the molar mass of the gas, in
kg
mol
The question is nonspecific for which gas, but we're just asked to find what generally happens to the r.m.s. speed if only the temperature changes, so we'll call the quantity
3
R
M
M
a constant,
k
:
u
rms-1
=
√
k
T
If the temperature is tripled, then this becomes
u
rms-2
=
√
3
k
T
To find what happens, let's divide this value by the original equation:
u
rms-2
u
rms-1
=
√
3
k
t
√
k
t
=
√
3
Thus, if the temperature is tripled, the root-mean-square speed of the gas particles increases by a factor of
√
3
.
Explanation: