Определите средний квадрат скорости движения молекул газа, если его масса 3 кг, объем 4,9 м3 и давление 105 Па. а) 1,2 • 105 м2/с2 г) 5,5 • 106 м2/с2 б) 2,8 • 103 м2/с2 д) 6,8 • 107 м2/с2 в) 4,9 • 105 м2/с2
The average square velocity of a gas molecule is calculated using the formula: v^2 = 3kT/m, where v is the average velocity, k is the Boltzmann constant, T is the temperature, and m is the mass of the molecule. In this case, we can use the ideal gas law, PV = nRT, to find the temperature: T = (PV)/(nR), where P is the pressure, V is the volume, n is the number of moles (which equals the mass of the gas divided by its molar mass), and R is the universal gas constant. Plugging in the values, we get T = (105 Pa * 4.9 m^3)/(3 kg / 0.029 kg/mol * 8.314 J/mol K) = 1669 K. Now, we can use this temperature to calculate the average square velocity: v^2 = (3 * 1.38 * 10^-23 J/K * 1669 K) / 3 kg = 5.5 * 10^6 m^2/s^2. Therefore, the correct answer is г) 5,5 • 106 м2/с2. Keep in mind that this assumes an ideal gas behavior and neglects the intermolecular forces between the gas molecules.
