Question

The average speed of a nitrogen molecule in air is proportional to the square root of the temperature in kelvins (K). If the average speed is 475 m/s on a warm summer day (temperature=300.0 K), what is the average speed on a frigid winter day (250.0 K)?

Answer 1

Answer:

v₂ = 395.83 m/s

Explanation:

given,

Average speed of nitrogen molecule, v₁ = 475 m/s

Temperature in summer, T₁ = 300 K

Average speed of nitrogen molecule in winter, v₂ = ?

Temperature in winter, T₂ = 250 K

The relation of average speed with temperature

          $v\ \alpha\ \sqrt{T}$

now,

        $\dfrac{v_2}{v_1} = \dfrac{\sqrt{T_2}}{\sqrt{T_1}}$

        $\dfrac{v_2}{475} = \dfrac{\sqrt{250}}{\sqrt{300}}$

                     v₂ = 0.833 x 475

                     v₂ = 395.83 m/s

The average speed on a frigid winter day is equal to v₂ = 395.83 m/s