The ratio of rms speed and most probable speed of molecules of an ideal gas is R at temperature T. If the temperature is increased by 2% then the percentage change in the ratio will be A) 2% B) 4% C) 3% 4)Zero
Answers
Given:
The ratio of rms speed and most probable speed of molecules of an ideal gas is R at temperature T. If the temperature is increased by 2%
To find:
The percentage change in the ratio
Solution:
To solve the given problem we will use the following formula of the root mean square speed and the most probable speed of a gas:
where R = gas constant = 8.314 kg m²/mol K s², T = temperature (K), M = molecular mass (kg/mol)
The ratio of root mean square speed and most probable speed of molecules of an ideal gas is R at temperature T
i.e.,
. . . . (1)
If the temperature is increased by 2%
Then the increased temperature, T' =
Therefore,
The new ratio (R') will be,
=
=
=
=
from (1), we get
= R . . . (2)
Now,
The percentage change in the ratio will be,
=
=
from (2), we get
=
= ← option (4)
Thus, the percentage change in the ratio will be → Zero.
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