Question

При какой температуре молекулы гелия имеют такую же среднюю квадратическую скорость малекулы водорода при 15градус с?

Answer 1

Запишем условие равенства их квадратичных скоростей: 3*K*Tв*Nа/Mв=3*K*Tг*Na/Mг, сокращаем на одни и те же величины в правой и левой части, получаем Тв/Мв=Тг/Мг, подставляя числовые значения, получаем. что Тг=288*0,004/0,002=576К.
t=576K-273K=303градусаС

Answer 2

Temperature for Equal Average Square Speed of Helium and Hydrogen Molecules

To find the temperature at which helium molecules have the same average square speed as hydrogen molecules at 15 degrees Celsius, we can use the formula for the average kinetic energy of gas molecules:

Average kinetic energy (KE) = (3/2) * k * T

Where: - k is the Boltzmann constant (1.38 x 10^-23 J/K) - T is the temperature in Kelvin

We can set up an equation to find the temperature at which helium and hydrogen molecules have the same average kinetic energy, and therefore the same average square speed.

Let's calculate it step by step.

First, we need to find the average square speed of hydrogen molecules at 15 degrees Celsius.

Average Square Speed of Hydrogen Molecules at 15°C

The average square speed of gas molecules can be calculated using the formula:

Average square speed (u^2) = (3 * k * T) / m

Where: - k is the Boltzmann constant - T is the temperature in Kelvin - m is the mass of the molecule

The molar mass of hydrogen (H2) is approximately 2.02 g/mol.

Converting 15 degrees Celsius to Kelvin: T = 15°C + 273.15 = 288.15 K

Now, let's calculate the average square speed of hydrogen molecules at 15°C.

Average square speed of hydrogen molecules at 15°C: u^2_hydrogen = (3 * k * T) / m_hydrogen

Now, we need to find the temperature at which helium molecules have the same average square speed as hydrogen molecules at 15 degrees Celsius.

Temperature for Equal Average Square Speed of Helium and Hydrogen Molecules

We can set up the equation:

(3/2) * k * T_helium = (3 * k * T_hydrogen) / m_hydrogen

Solving for T_helium:

T_helium = (3 * T_hydrogen * m_hydrogen) / (2 * m_helium)

Where: - T_helium is the temperature for helium - T_hydrogen is the temperature for hydrogen - m_helium is the molar mass of helium (approximately 4.00 g/mol)

Now, let's calculate the temperature at which helium molecules have the same average square speed as hydrogen molecules at 15 degrees Celsius.

T_helium = (3 * 288.15 K * 2.02 g/mol) / (2 * 4.00 g/mol)

T_helium ≈ 216.11 K

So, at approximately 216.11 Kelvin, the molecules of helium have the same average square speed as the molecules of hydrogen at 15 degrees Celsius.