The New Student's Reference Work/Charles, Law of

Charles, Law of. When a constant mass of gas is heated, either or both of two things may happen to it. (1) The effect may be to increase the volume of the gas while the pressure remains the same; (2) the effect may be to increase the pressure of the gas while the volume remains constant; or (3) both the volume and the pressure may be changed simultaneously. Charles' law, which might more properly be called Gay-Lussac's law, tells us just how these changes take place. If the mass and pressure of the gas remain constant, then the volume of the gas increases ¹⁄₂₇₃ part for each degree centigrade through which it is heated. Thus, if we denote by V₀ the volume of the gas at the temperature of melting ice, its volume at any other temperature, V_t, will be given by the following equation:

V_t = V₀[1 + 0.003665 t⁰]
= V₀[1 + ^t⁄₂₇₃]

The fact thus described is known as Charles' law. If the volume remains constant and the pressure changes, the effect is described by the following equation:

P_t = P₀[1 + 0.003665 t⁰]

where P₀ is the pressure at the temperature of melting ice and P_t the pressure at t⁰. If pressure and volume both change, then

P_tV_t = P₀V₀[1 + 0.003665 t⁰]

The student should be warned that this law of Charles is very accurately true for all gases throughout a moderate range of pressures, but is not exactly true for any gas, and does not hold at all in the case of vapors.