Q117 / 200 · NEET 2023 (All India) · Physics

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?

A
$223 K$
B
$669 ° C$
Correct answer
C
$3295 ° C$
D
$3097 K$

Solution

RMS speed is given by, $v = \sqrt{\frac{3 R T}{M}}$ .
Therefore,
$v \propto \sqrt{T}$ .
Given:
Initial temperature, $T_{1} = (- 50 + 273) K = 223 K$
Let, initial speed be $v$ , then final speed will be $v + 3 v = 4 v$ .
Now,
$\frac{4 v}{v} = \sqrt{\frac{T_{2}}{T_{1}}} \Rightarrow T_{2} = 16 T_{1} = 3568 K = (3568 - 273) ° C = 3295 ° C$

Hence, the correct answer is option: 'C'.

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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?

Solution

More Kinetic Theory of Gases Questions

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?