NEET 2023 — Physics solution

NEET2023Physics

The temperature of a gas is $- 5 0^{\circ}$ C. To what temperature the gas should be heated so that the rms speed is increased by $3$ times?

Solution

$v_{r m s} \propto T$ . The phrase "increased by $3$ times" means the final speed is $v + 3 v = 4 v$ .

Initial $T_{1} = - 50 + 273 = 223$ K. Taking the ratio:

$\frac{v _{1}}{v _{2}} = \frac{T _{1}}{T _{2}} \Rightarrow \frac{v}{4 v} = \frac{223}{T _{2}}$

$\Rightarrow T_{2} = 16 \times 223 = 3568$ K $= 329 5^{\circ}$ C.

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