##### Gay-Lussac's Law:

Gay-Lussac's Law states that the pressure of a fixed amount of gas at fixed volume is
directly proportional to its temperature in kelvins.

#### Gay-Lussac's Law Formula :

Gas Equation: P_{i}/T_{i} = P_{f} / T_{f}
Initial Pressure(P_{i}) = P_{f}T_{i} / T_{f}
Initial Temperature(T_{i}) = P_{i}T_{f} / P_{f}
Final Pressure(P_{f}) = P_{i}T_{f} / T_{i}
Final Temperature(T_{f}) = P_{f}T_{i} / P_{i}
**where,**
P_{i} = Initial Pressure,
T_{i} = Initial Temperature,
P_{f} = Final Pressure.
T_{f} = Final Temperature
##### Gay-Lussac's Law Example

Case 1: A cylinder contain a gas which has a pressure of 125kPa at a temperature of 200 K. Find the temperature of the gas which has a pressure of 100 kPa.

P_{i} = 125 kPa, T_{i} = 200 K, P_{f} = 100 kPa

##### Step 1:

Substitute the values in the below final temperature equation: Final Temperature(T_{f}) = P_{f}T_{i} / P_{i}
= (100 x 200) / 100
= 20000 / 125
Final Temperature(T_{f}) = 160 K
This example will guide you to calculate the final temperature manually.
Case 2: Find the final pressure of gas at 150 K, if the pressure of gas is 210 kPa at 120 K.
P_{i} = 210 kPa, T_{i} = 120 K, T_{f} = 150 K

##### Step 1:

Substitute the values in the below pressure equation:

Final Pressure(P

_{f}) = P

_{i}T

_{f} / T

_{i}
= (210 x 150) / 120
= 31500 / 120
Final Pressure(V

_{f}) = 262.5 kPa
This example will guide you to calculate the pressure manually.