Which equation represents the combined gas law?
P1V1=P2V2
V1/T1= V2/T2
P1V1/T1= P2V2/T2
P1 V1 T1 = P2 V2 T2
The Correct Answer and Explanation is :
The combined gas law is represented by the equation:
[ P_1 V_1 / T_1 = P_2 V_2 / T_2 ]
This equation combines three individual gas laws: Boyle’s law, Charles’s law, and Gay-Lussac’s law, allowing for the examination of the relationships between pressure (P), volume (V), and temperature (T) of a given amount of gas.
Explanation
1. Boyle’s Law: This law states that for a given mass of gas at constant temperature, the pressure and volume of the gas are inversely proportional. Mathematically, it can be expressed as:
[ P_1 V_1 = P_2 V_2 ]
This implies that if the volume of a gas decreases, the pressure increases, provided the temperature remains constant.
2. Charles’s Law: This law describes how gases tend to expand when heated. It states that the volume of a gas is directly proportional to its temperature (measured in Kelvin) when pressure is held constant:
[ V_1/T_1 = V_2/T_2 ]
Thus, if the temperature of a gas increases, its volume will also increase, assuming pressure remains unchanged.
3. Gay-Lussac’s Law: This law states that the pressure of a gas is directly proportional to its absolute temperature when volume is held constant:
[ P_1/T_1 = P_2/T_2 ]
This means that increasing the temperature of a gas while keeping the volume constant will result in an increase in pressure.
The Combined Gas Law: By combining these individual laws, the combined gas law allows us to analyze changes in the state of a gas when pressure, volume, and temperature change simultaneously. The equation ( P_1 V_1 / T_1 = P_2 V_2 / T_2 ) can be rearranged to solve for any of the variables (P, V, or T) given the other values, which is especially useful in various scientific and engineering applications where gas behavior needs to be predicted or controlled. This law assumes that the amount of gas remains constant, making it a powerful tool for understanding gas dynamics in various contexts.