Question 974: Thermodynamics & KTG

Question

The temperature of a gas is $$-50^{\circ} \mathrm{C}$$. To what temperature the gas should be heated so that the rms speed is increased by $$3$$ times?

Accepted Answer

$$v_{\mathrm{rms}} \propto \sqrt{T}$$
$$\frac{\mathrm{v}_{1}}{\mathrm{v}_{2}}=\sqrt{\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}}$$
$$=$$ let initial speed is $$\mathrm{v}$$
As speed is increased by $$3$$ times so final speed become $$4 v$$
$$\Rightarrow \frac{\mathrm{v}}{4 \mathrm{v}}=\sqrt{\frac{223}{\mathrm{~T}}}$$
$$\mathrm{T}=3568 \mathrm{~K}$$
So temp. in $${ }^{\circ} \mathrm{C}=3568-273=3295^{\circ} \mathrm{C}$$

Answer

$$3295^{\circ} \mathrm{C}$$

Answer

$$3097 \mathrm{~K}$$

Answer

$$223 \mathrm{~K}$$

Answer

$$669^{\circ} \mathrm{C}$$

Thermodynamics & KTG

The temperature of a gas is $-50^{\circ} \mathrm{C}. To what temperature the gas should be heated so that the rms speed is increased by 3$ times?

Choose the correct answer: