Question

0.014 kg of nitrogen is enclosed in a vessel at a temperature of 27°C. How much heat has to be transferred to the gas to double the rms velocity of its molecules?

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

Answer 1

Answer: (A)

1200 K

Answer 2

Using, $V_{rms} = \sqrt{\frac{3RT}{m}}$

or $\frac{(V_{rms})}{(V_{rms})} = \sqrt{\frac{T_{1}}{T_{2}}}$ ($\because$R and m are constant)

According to questions,

$(V_{rms}) = 2(V_{rms})_{1}$

$\therefore\frac{(V_{rms})_{1}}{2(V_{rms})_{1}} = \sqrt{\frac{300}{T_{2}}}$

$\Rightarrow \frac{1}{4} = \frac{300}{T_{2}}$

$T_{2} = 300 \times 4 = 1200K$