Question 823: Thermodynamics & KTG

Question

The temperature of a gas is $$-68^{\circ} \mathrm{C}$$. To what temperature should it be heated, so that the r.m.s. velocity of the molecules be doubled?

Accepted Answer

$$\mathrm{T}_1=-68{ }^{\circ} \mathrm{C}=-68+273 \mathrm{~K}=205 \mathrm{~K}$$
R.M.S. velocity, $$\mathrm{v}_{\mathrm{rms}} \propto \sqrt{\mathrm{T}}$$
$$\begin{array}{ll} 
& \frac{\left(\mathrm{v}_{\mathrm{ms}}ight)_2}{\left(\mathrm{v}_{\mathrm{ms}}ight)_1}=\sqrt{\frac{\mathrm{T}_2}{\mathrm{~T}_1}}=2 \
	herefore \quad & \frac{\mathrm{T}_2}{\mathrm{~T}_1}=4 \
	herefore \quad & \mathrm{T}_2=4 	imes 205=820 \mathrm{~K} \
	herefore \quad & \mathrm{T}_2=547^{\circ} \mathrm{C}
\end{array}$$

Answer

$$357^{\circ} \mathrm{C}$$

Answer

$$457^{\circ} \mathrm{C}$$

Answer

$$547^{\circ} \mathrm{C}$$

Answer

$$820^{\circ} \mathrm{C}$$

Thermodynamics & KTG

The temperature of a gas is $-68^{\circ} \mathrm{C}$. To what temperature should it be heated, so that the r.m.s. velocity of the molecules be doubled?

Choose the correct answer: