# Combined Gas Law

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

Combined gas law is the relationship between pressure volume and temperature for a system with a constant amount of gas.  This law comes from the combination of three different laws: Boyle's Law, Charle's Law, and Gay-Lussac's Law.

## Combined Gas Law formula

 $$\large{ \frac{ p_1\;V_1 }{ T_1 } = \frac{ p_2\;V_2 }{ T_2 } }$$

### Where:

$$\large{ p_1 }$$ = pressure of the gas under conditions

$$\large{ T_1 }$$ = temperature of the gas under conditions

$$\large{ V_1 }$$ = volume of the gas under conditions

$$\large{ p_2 }$$ = pressure of the gas under conditions

$$\large{ T_2 }$$ = temperature of the gas under conditions

$$\large{ V_2 }$$ = volume of the gas under conditions

### Solve for:

 $$\large{ p_1 = \frac{ p_2 \; T_1 \; V_2 }{ T_2 \; V_1 } }$$ $$\large{ p_2 = \frac{ p_1 \; T_2 \; V_1 }{ T_1 \; V_2 } }$$ $$\large{ T_1 = \frac{ p_1 \; T_2 \; V_1 }{ p_2 \; V_2 } }$$ $$\large{ T_2 = \frac{ p_2 \; T_1 \; V_2 }{ p_1 \; V_1 } }$$ $$\large{ V_1 = \frac{ p_2 \; T_1 \; V_2 }{ T_2 \; p_1 } }$$ $$\large{ V_2 = \frac{ p_1 \; T_2 \; V_1 }{ p_2 \; T_1 } }$$