Helium occupies a volume of 0.04m3 at a pressure of 2*10^5 PA and temperature of 27 degree Celsius.Calculate the rms speed of its molecule and the average translational kinetic energy of one of this gas.

To calculate the Root Mean Square (RMS) speed of helium molecules and the average translational kinetic energy, we can use the ideal gas law and the equation for calculating kinetic energy.

1. First, let's convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 27 + 273.15 = 300.15 K

2. We can use the ideal gas law equation to find the number of moles (n) of helium:
PV = nRT
n = PV / RT
where P is the pressure, V is the volume, R is the ideal gas constant (8.314 J/(mol·K)), and T is the temperature in Kelvin.

n = (2 * 10^5 Pa) * (0.04 m^3) / (8.314 J/(mol·K) * 300.15 K)

3. Now that we have the number of moles of helium, we can calculate the mass of one helium molecule (m) using its molar mass:
Molar mass of helium (M) = 4.0026 g/mol
m = M / Avogadro's constant (6.02214 x 10^23 molecules/mol)

4. The RMS speed (v_rms) of the helium molecules can be calculated using the equation:
v_rms = sqrt(3 * k * T / m)
where k is the Boltzmann constant (1.380649 x 10^-23 J/K), T is the temperature in Kelvin, and m is the mass of one helium molecule.

5. The average translational kinetic energy (E_avg) of one helium molecule can be calculated using the equation:
E_avg = (3/2) * k * T

Now we can substitute the values into the formulas and calculate the answers.

Calculating the RMS speed (v_rms):
v_rms = sqrt(3 * k * T / m)

Calculating the average translational kinetic energy (E_avg):
E_avg = (3/2) * k * T

Note: Make sure to use the appropriate units for all the quantities.