Kinetic Theory Of Gases Question 47
Question: In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on T as $ {{\text{T}}^{\text{q}}} $ . A good estimate for q is:
Options:
A) $ \frac{1}{2} $
B) 2
C) 1
D) $ \frac{1}{4} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Pressure, $ P=\frac{1}{3}\frac{mN}{V}V _{rms}^{2} $
$ \text{or, }P=\frac{( mN )T}{V} $ If the gas mass and temperature are constant then $ P\propto {{(V _{rms})}^{2}}\propto T $ So. force $ \propto {{(V _{rms})}^{2}}\propto T $ i.e., Value of $ q=1 $
BETA
