For a fixed amount of gas, temperature changes produce simple pressure or volume changes when another mechanical variable is held fixed. The temperature must be measured on an absolute scale, such as kelvins.

At constant pressure, Charles's law states that gas volume is proportional to absolute temperature:

$$V\propto T,$$

so

$$\boxed{\frac{V_1}{T_1}=\frac{V_2}{T_2}}.$$

At constant volume, the pressure is proportional to absolute temperature. This relation is commonly called Amontons's law or the pressure-temperature gas law:

$$p\propto T,$$

so

$$\boxed{\frac{p_1}{T_1}=\frac{p_2}{T_2}}.$$

Example: constant pressure

A flexible container holds $1.20,\mathrm L$ of gas at $300,\mathrm K$. If pressure and amount remain constant while the gas is heated to $375,\mathrm K$,

$$V_2=V_1\frac{T_2}{T_1} =(1.20,\mathrm L)\frac{375}{300} =1.50,\mathrm L.$$

Why Celsius cannot be used directly

If $27,^\circ\mathrm C$ were doubled numerically to $54,^\circ\mathrm C$, the absolute temperature would not double: the corresponding temperatures are about $300,\mathrm K$ and $327,\mathrm K$. Gas-law proportionalities therefore require kelvins.

These relations apply to equilibrium states for the same fixed amount of gas. Charles's and Amontons's laws are not independent of the ideal-gas law; each is a constrained case of the same general pressure-volume-temperature-amount relation.