Kinetic Theory Of Gases Question 66
Question: One kg of a diatomic gas is at a pressure of $ 8\times 10^{4}N/m^{2}. $ The density of the gas is4kg/m3. What is the energy of the gas due to its thermal motion?
Options:
A) $ 5\times 10^{4}J $
B) $ 6\times 10^{4}J $
C) $ 7\times 10^{4}J $
D) $ 3\times 10^{4}J $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ \text{Volume=}\frac{\text{mass}}{\text{density}}=\frac{1}{4}m^{3} $
$ \text{K}\text{.E}\text{.}=\frac{5}{2}PV=\frac{5}{2}\times 8\times 10^{4}\times \frac{1}{4}=5\times 10^{4}J $ Alternatively: $ \text{K}\text{.E}\text{.}=\frac{5}{2}nRT=\frac{5}{2}\frac{m}{M}RT=\frac{5}{2}\frac{m}{M}\times \frac{PM}{d} $
$ [ \
Therefore PM=dRT ] $
$ =\frac{5}{2}\frac{mP}{d}=\frac{5}{2}\times \frac{1\times 8\times 10^{4}}{4}=5\times 10^{4}J $
BETA
