The temperature of a gas is -50°C. To what temperature the gas should be heated so that the rms speed is increased by 3 times? [2023]

Question

The temperature of a gas is -50°C. To what temperature the gas should be heated so that the rms speed is increased by 3 times? [2023]

Smart Achievers · Accepted Answer

(4)

As we know that $v_{rms} \propto \sqrt{T}$

$\Rightarrow \frac{{(v_{rms})}_{2}}{{(v_{rms})}_{1}} = \sqrt{\frac{T_{2}}{T_{1}}} \Rightarrow 4 = \sqrt{\frac{T}{273 - 50}}$

$\Rightarrow 16 = \frac{T}{223} \Rightarrow T = 3568 K = 3568 - 273 = 3295 ° C$

$∴$ $Δ T = 3295 ° C$

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