What does the equation P/T = k represent?

The equation P/T = k represents the relationship between pressure and temperature, where P stands for pressure, T for temperature, and k is a constant for a given amount of gas at a constant volume. This relationship is derived from the ideal gas law, which describes how these variables are interconnected.

In the context of this equation, as the temperature of a gas increases, assuming that the volume remains constant, the pressure also increases. This reflects Lord Kelvin's understanding of gas behavior, illustrating that temperature directly influences the kinetic energy of gas particles, leading to an increase in pressure. Thus, this equation is crucial in thermodynamics and helps articulate the concepts of gas behavior under varying thermal conditions.