The air temperature in the room changed from 7 to 27 ° C. By what percentage has the number

The air temperature in the room changed from 7 to 27 ° C. By what percentage has the number of molecules in the room decreased?

We will start by recalling Boltzmann’s law, since we will need it to solve the problem:

p = nkT,

where n is the volumetric concentration of molecules, which can be calculated by the formula:

n = N / V.

Let’s write Boltzmann’s law: p = N / V * k * T.

We express the total number of molecules from the formula:

N = (pV) / (kT).

We just have to substitute the values and calculate the ratio:

N27 / N7 = pV / kT27: pV / kT7 = T7 / T27 = (273 + 7) / (273 + 27) = 280/300 = 28/30 = 14/15 = 1 – 1/15 = 100% – 100 % / 15 = 100% – 6 2/3% = 100% – 6.67%.

Answer: by 6.67%