The average velocity of molecules of nitrogen gas (N2) at room temperature is around 500 m/s. If you were to raise the temperature of the nitrogen gas by 50°C what is a good estimate for the speed of the molecules?

The average velocity of molecules of nitrogen gas (N2) at room temperature is around 500 m/s. If you were to raise the temperature of the nitrogen gas by 50°C what is a good estimate for the speed of the molecules?

To estimate the speed of the molecules of nitrogen gas (N2) at the new temperature, we can make use of the kinetic theory of gases. According to this theory, the average kinetic energy of gas molecules is directly proportional to the temperature of the gas.

To calculate the new speed of the molecules, we can use the formula v_new = v_initial * sqrt(T_new/T_initial), where v_initial is the initial speed of the molecules, T_initial is the initial temperature, T_new is the new temperature, and v_new is the new speed.

Given that the average velocity (speed) of the molecules of nitrogen gas at room temperature is 500 m/s, we need to determine the new speed when the temperature is increased by 50°C.

To perform the calculation, we'll convert the temperature from Celsius to Kelvin since the temperature must be in Kelvin for the formula to work properly. The conversion from Celsius to Kelvin is T(K) = T(°C) + 273.15.

Let's calculate the new speed using the formula:

v_new = 500 m/s * sqrt((T_initial + 50 + 273.15) / (T_initial + 273.15))

Assuming the initial temperature is around 25°C, we can plug in the values:

v_new = 500 m/s * sqrt((25 + 50 + 273.15) / (25 + 273.15))

Now we can solve this equation to get the estimate for the new speed of the molecules of nitrogen gas.