Question

0.014 kg of nitrogen is enclosed in a vessel at ${27}^{o}C$. The heat given to gas in order to double its rms speed is

• A. 2.25 kcal
• B. 4.50 kcal
• C. 1.15 kcal
• D. 2 kcal

Answer 1

The correct option is A 2.25 kcal

As we know,
RMS speed is

$U=\sqrt{\frac{3RT}{M}}$

given,

$\frac{(U_{rms}{)}_2}{(U_{rms}{)}_t}=\sqrt{\frac{T_2}{T_1}}$

$2=\sqrt{\frac{T_2}{T_1}}$

$\therefore T_2=4T_1=4\times 300=1200K$

Also, $Q_v=n\times C_v\times dT$

$=\frac{0.014\times {10}^3}{28}\times \frac{5}{2}R\times 900$

$=2.250\times {10}^{3}cal$