Question

$0.014$kg of nitrogen is enclosed in a vessel at a temperature of ${27}^o$C. At which temperature the rms velocity of nitrogen gas is twice its the rms velocity at ${27}^o$C?

• A. $1200$K
• B. $600$K
• C. $300$K
• D. $150$K

Answer 1

The correct option is A $1200$K

Using, $v_{rms}=\sqrt{\frac{3RT}{m}}$
or $\frac{(v_{rms}{)}_1}{(v_{rms}{)}_2}=\sqrt{\frac{T_1}{T_2}}$ ($\because$ R and m are constant)
According to question, $(v_{rms}{)}_2=2(v_{rms}{)}_1$

$\therefore \frac{(v_{rms}{)}_1}{2(v_{rms}{)}_1}=\sqrt{\frac{300}{T_2}}\Rightarrow \frac{1}{4}=\frac{300}{T_2}$

$T_2=300\times 4=1200$K