Question

The density of a gas filled in an electric lamp is $0.75\text{kg}/{\text{m}}^3$ . After the lamp has been switched on, the pressure in it increases from $4\times {10}^4\text{Pa}$ to $9\times {10}^4\text{Pa}$. What is the increase in $U_{RMS}$ ?

• A. 100 m/s
• B. 200 m/s
• C. 300 m/s
• D. None of these

Answer 1

The correct option is B 200 m/s

$d=\frac{PM}{RT}\therefore 0.75=\frac{4\times {10}^4\times M_{\left(kg\right)}}{R{T}_1}$
$(\therefore u_{rms}=\sqrt{\frac{3RT}{M}})$
$\therefore \frac{R{T}_1}{M}=\frac{4\times {10}^4}{0.75}$
$\Rightarrow \frac{3R{T}_1}{M}=16\times {10}^4$
$\Rightarrow u_{rms,initial}=4\times {10}^{2}m/s$
Similarly, $u_{rms,final}=\sqrt{\frac{3\times 9\times {10}^4}{0.75}}=6\times {10}^{2}m/s$
$\therefore \text{increase}=600-400=200m/s.$