Question

When the temperature of an ideal gas is increased from 27°C to 227°C, its speed is changed from 400 ms^-1 to v_s, and Then v_s is ______.

पर्याय

• 516 ms^-1

• 450 ms^-1

• 310 ms^-1

• 746 ms^-1

Answer 1

When the temperature of an ideal gas is increased from 27°C to 227°C, its speed is changed from 400 ms^-1 to v_s, and Then v_s is 516 ms^-1.

Explanation:

We know that rms speed is directly proportional to the square root of temperature.

v_rms ∝ `sqrtT`

Hence, `"v"_{rms(1)}/"v"_{rms(2)} = sqrt(T_1/T_2)`

Given, T₁ = 27°C = (27 + 273) = 300 K

T₂ = 227°C = (227 + 273) = 500 K

`"v"_{rms(2)}` = 400 ms^-1

⇒ `"v"_{rms(1)}/"v"_{rms(2)} = sqrt(300/500)`

⇒ `"v"_{rms(2)} = sqrt(500/300)"v"_{rms(1)}`

⇒ v_s = 516 ms^-1 `[∵ "v"_{rms_2} = "v"_s]`