At a temperature of 27 degrees Celsius, the rarefied air pressure in a miniature X-ray tube is 25 MPa.

At a temperature of 27 degrees Celsius, the rarefied air pressure in a miniature X-ray tube is 25 MPa. The volume of the tube is 5×10 to minus 6 degrees (m3). The molar mass of air is 0.029 (kg / mol). What is the mass of air in the tube?

Let’s turn to the Mendeleev-Clapeyron equation:

p * v = m / M * R * T, where p is pressure, v is volume, m is gas mass, M is molar mass, R is universal gas constant, T is temperature.

We express from this formula the mass of gas (T = 300 K):

m = P * v * M / R * T.

We substitute the known values:

m = 25 * 10 ^ (- 3) * 5 * 10 ^ (- 6) * 0.029 / 8.31 * 300 = 125 * 0.029 * 10 ^ (- 11) / 8.31 * 3 = 0.145 * 10 ^ ( -11) kg.

Answer: the required mass is 0.145 * 10 ^ (- 11) kg.