Question

Assertion :The fraction of molecules having speed in the range $u$ and $(u+du)$ of a gas of molar mass $M$ at temperature $T$ is the same as that of gas of molar mass of $2M$ and temperature $2T$. Reason: The fraction of molecules having their speed within the range $u$ to $(u+du)\propto \frac{M}{T}$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

The fraction of gaseous molecules having their speed within the range $u$ to $(u+du)$ is given by the expression $\frac{d{N}_u}{dt}=4\pi \left(\frac{M}{2\pi RT}{)}^{3/2}exp\right(-M{u}^2/2RT)u^{2}du$.
As long as the ratio $\frac{M}{T}$ is constant, the fraction of molecules having speed in the range $u$ and $(u+du)$ of a gas will be same.
Thus, Assertion is correct but Reason is incorrect.
Hence, the option C is the correct answer.