On top of Mount Everest, the temperature is -19 ∘C in July. Being a physicist, you determine by how many degrees Celsius one needs to change the air temperature to double the average kinetic energy of its molecules. Part A Being a physicist, you determine by how many degrees Celsius one needs to change the air temperature to double the average kinetic energy of its molecules. ΔT = nothing ∘C

254 °C

Explanation:

The average kinetic energy of gas molecules K = 3RT/2N where R = gas constant = 8.314 J/mol-K, N = avogadro's constant = 6.022 × 10²³ atoms/mol

T = temperature in Kelvin.

Let K be its average kinetic energy at t = -19°C = 273 + (-19) = 273 - 19 = 254 K = T. K = 3RT/2N = 3 × 8.314 J/mol-K × 254 K/(2 × 6.022 × 10²³ atoms/mol) = 5.26 × 10⁻²¹ J

When its average kinetic energy doubles, it becomes K₁ = 2K = 2 × 5.26 × 10⁻²¹ = 10.52 × 10⁻²¹ J at temperature T₂. So,

K₁ = 3RT₁/2N

T₁ = 2NK₁/3R

T₁ = 2 × 6.022 × 10²³ atoms/mol × 10.52 × 10⁻²¹ J/3 × 8.314 J/mol-K = 508 K

The temperature difference is thus ΔT = T₁ - T = 508 K - 254 K = 254 K.

Since temperature change in kelvin scale equals temperature change in Celsius scale ΔT = 254 °C

So, we need to change the temperature of the air by 254 °C to double its average kinetic energy.

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