Question

В аудитории объемом 90 кубометров температура воздуха повысилась с 20 ℃ до 28℃. Атмосферное давление нормальное, молярная масса воздуха 0,029 кг/моль, какая масса воздуха вышла из комнаты.

Answer 1

По закону Менделеева-Клапейрона имеем:

$PV= \frac{mRT}{M}$,

откуда выражаем формулу для массы:

$m= \frac{PVM}{RT}$

тогда масса, вышедшая из комнаты, равна:

$зm= \frac{PVM}{R}( \frac{1}{ T_{1} }-\frac{1}{ T_{2} }) \\ \\ зm= \frac{ 10^{5}*90*29* 10^{-3} }{8,31}( \frac{1}{293} - \frac{1}{301}) \\ \\ зm=31,407* 10^{3}* 9 * 10^{-5} \\ \\ зm= 2,82 kg$

Answer 2

Calculating the Mass of Air That Left the Room

To calculate the mass of air that left the room when the temperature increased from 20°C to 28°C in a 90 cubic meter room, we can use the ideal gas law equation:

PV = nRT

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

First, we need to calculate the initial and final number of moles of air in the room.

Initial Number of Moles of Air

The initial number of moles of air can be calculated using the ideal gas law equation. Given: - Initial temperature (T1) = 20°C = 293.15 K (temperature in Kelvin) - Volume (V) = 90 cubic meters - Atmospheric pressure is considered normal - Molar mass of air (M) = 0.029 kg/mol

Using the ideal gas law equation, we can solve for the initial number of moles (n1):

n1 = PV / RT1

Where: - P = atmospheric pressure - R = ideal gas constant (8.314 J/(mol·K))

Final Number of Moles of Air

The final number of moles of air can be calculated using the same ideal gas law equation, but with the final temperature (T2) = 28°C = 301.15 K.

n2 = PV / RT2

Calculating the Mass of Air That Left the Room

Once we have the initial and final number of moles of air, we can calculate the mass of air that left the room using the difference between the initial and final number of moles.

Mass of air that left the room = (n1 - n2) * M

Where: - n1 = initial number of moles of air - n2 = final number of moles of air - M = molar mass of air

Let's calculate the initial and final number of moles of air using the given data.