Question

As per kinetic theory of gases which of the following statements is/are true?
a) Temperature of a gas is a measure of average kinetic energy of a molecule
b) Temperature of a gas depends on the nature of the gas
c) Heavier molecule has lower average speed
d) Lighter molecule has lower average speed

• A. a & b are true
• B. b & c are true
• C. a & c are true
• D. b & d are true

Answer 1

Answer: (C)

As per kinetic theory of gases,
Statement I Since, average kinetic energy of gases, $K{E}_{av}=\frac{3}{2}{K}_{B}T$
$\therefore K{E}_{av}\propto T$
Hence, temperature of gases is a measure of average kinetic energy of a molecule is correct.
So, option (a) is the correct.
Statement II As temperature of gas is independent of nature of gas.
Hence, option (b) is the incorrect.
Statement III Since, $v_{rms}=\sqrt{\frac{3RT}{M}}$
where, $v_{\text{rms }}=$ root mean square speed,
$R=$ universal gas constant
$T=$ temperature
and $M=$ molar mass .
$\because v_{rms}\propto \frac{1}{\sqrt{M}}$
As $M$ increases $v_{\text{rms }}$ decreases.