A cylinder with a volume of 2m3 contains 2 kg of molecular nitrogen at a pressure of 100 kPa.

A cylinder with a volume of 2m3 contains 2 kg of molecular nitrogen at a pressure of 100 kPa. What is the temperature of this gas on the Celsius scale?

Let’s use the equation of state for an ideal gas:

p * V = m * R * T: M;

Let us express the value of T:

T = p * V * M: m * R, where p is the gas pressure; V is the volume; M is the molar mass of nitrogen;

m is the mass; R is the universal gas constant.

Given: p = 100 kPa, V = 2 m³, m = 2 kg, M = 0.028 kg / mol, R = 8.314 J / mol * K.

Decision:

T = 100 * 10³ * 2 * 0.028: 2 * 8.314 = 5.6 * 10³: 16.628 = 337 (K);

T = 337 K = 64 ° C.

Answer: The gas temperature is 64 ° C.