Question

Температура воздуха в комнате изменилась от 7 до 27 на сколько процентов уменьшилось число молекул в комнате

Answer 1

Дано: T₁ = 280 K, T₂ = 300 K
Найти: ΔN × 100% - ?
Решение:
$\boxed{p = nkT} \ ; \ n = \dfrac{N}{V}\ ; \ \rightarrow \ p = \dfrac{NkT}{V} \ ; \ N = \dfrac{pV}{kT} \\ \\ \dfrac{N_{2}}{N_{1}} = \dfrac{pV*kT_{1}}{kT_{2} * pV} = \dfrac{T_{1}}{T_{2}} = \dfrac{280 K}{300K} = \dfrac{14}{15} \\ \\ 15 \ \rightarrow \ 100\% \\ 14 \ \rightarrow \ x\% \\ \\ x = \dfrac{14*100\%}{15} = 93.33\% \\ \\ 100\% - 93.33\% = 6.67\%$
Ответ: Число молекул уменьшилось на 6.67%

Answer 2

Calculating the Percentage Change in the Number of Air Molecules

To calculate the percentage change in the number of air molecules in the room as the temperature changes from 7°C to 27°C, we can use the ideal gas law, which states that the number of molecules in a gas is directly proportional to the temperature. The formula for the ideal gas law is:

PV = nRT

Where: - P = pressure - V = volume - n = number of moles of gas - R = ideal gas constant - T = temperature in Kelvin

Since the volume of the room remains constant, we can simplify the formula to:

n1 / T1 = n2 / T2

Where: - n1 = initial number of molecules - T1 = initial temperature in Kelvin - n2 = final number of molecules - T2 = final temperature in Kelvin

Calculation

Given: - Initial temperature, T1 = 7°C - Final temperature, T2 = 27°C

Converting temperatures to Kelvin: - T1 = 7°C + 273.15 = 280.15 K - T2 = 27°C + 273.15 = 300.15 K

Using the formula: n1 / 280.15 = n2 / 300.15

Solving for the percentage change in the number of molecules: Percentage Change = ((n1 - n2) / n1) * 100

Result

The percentage change in the number of air molecules in the room as the temperature changes from 7°C to 27°C can be calculated using the above formula.