Answer to Question #118600 in Molecular Physics | Thermodynamics for Susan Williams

Question

State the pressure law and describe an experiment to verify it. Deduce the formula for the pressure coefficient of gas. What is this value?

Answer 1

At a constant volume, if the mass of the gas does not change, the pressure is directly proportional to the temperature:

$$p=kT.$$

Indeed, from the ideal gas law:

$$p_T=p_0(1+\beta T),\\ 1+\beta T=\frac{p_T}{p_0},\\ \beta=\frac{p_T-p_0}{p_0 T}.$$

The value depends on the temperature and pressure.

The experiment: take a heater, manometer, and chamber of fixed volume, heat the gas, measure the pressure at different temperatures. Then we can plot linear function p=kT.