Question

If $15\text{g}$ mass of nitrogen gas is enclosed in a vessel at a temperature ${27}^{\circ }\text{C}$. Amount of heat transfered to the gas, so that rms velocity of molecules is doubled is about
[Take $R=8.3\text{J/K mole}$]

• A. $\text{14 kJ}$
• B. $\text{6 kJ}$
• C. $\text{0.9 kJ}$
• D. $\text{10 kJ}$

Answer 1

The correct option is D $\text{10 kJ}$

Given that,
$T=27+273=300\text{K}$
$m=15\text{g}$
$M=28\text{g}$

Heat transferred in closed vessel is given by,
$Q=n{C}_v\Delta T.....\left(1\right)$

Rms speed is given by
$V_{rms}=\sqrt{\frac{3RT}{M}}$
$V_{rms}\propto \sqrt{T}$

As Rms speed is doubled, the temperature will be quadrupled
$T^{\prime }=4T$

For diatomic gas
${\gamma }_{diatomic}=\frac{7}{5}$
and
$C_v=\frac{5}{2}R$


Putting all the values in the equation $1$
$Q=n{C}_v\Delta T=\frac{15}{28}\times \frac{5R}{2}\times (4T-T)$
$Q=\frac{15}{28}\times \frac{5\times 8.3}{2}\times 3\times 300$
$Q=10000\text{J}=10\text{kJ}$