In a bottle with a capacity of 26 liters. there is 1.1 kg of nitrogen at a pressure of 35 at. determine the gas temperature

Given:
V = 26 l;
m = 1.1 kg;
p = 35 at ≈ 35.5 10⁵ Pa;
T -?

Solution:

According to the Mendeleev-Clapeyron law:
p V = m R T / M;

Let’s translate the capacity of the cylinder from liters to cubic meters:

26 l = 26 * 10⁻³ m³;

T = p * V * M / (m * R);

Knowing the molecular weight of the nitrogen molecule 28 * 10⁻³ kg / mol, we find the temperature:

T = 35.5 * 10⁵ * 26 * 10⁻³ * 28 * 10⁻³ / (1.1 * 8.31) ≈ 283 K or t = 283-273 = 10 ° C.

Answer: gas temperature 10 ° C.