Which equation represents the combined gas law?
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The correct option is P1V1 / T1 = P2V2 /T2.
The combine gas law states that the ratio of the product of pressure, volume and absolute temperature of a gas is always a constant. Mathematically, the law is represented by P1V1 / T1 = P2V2 /T2; where
P1 and P2 = Initial and final pressure of the gas
V1 and V2 = Initial volume and the final volume of the gas
T1 and T2 = Initial temperature and final temperature of the gas.
Combine gas law was formed by the combination of Boyle's law, Charles' law and Gay Lussac's law.
Explanation :
Combined gas law comes from the combination of Boyle's law, Charles law and Gay Lussac's law.
According to Boyle's law,
At constant temperature, pressure of a gas is inversely proportional to its volume.
i.e. [tex]P\propto\dfrac{1}{V}[/tex]
[tex]PV=constant[/tex]..........(1)
Where,
P is the pressure of gas
V is the volume of gas
According to Charles law,
At constant pressure, volume of a gas is directly proportional to its temperature.
i.e. [tex]V\propto T[/tex]
[tex]\dfrac{V}{T}=constant[/tex]..............(2)
Where, T is the temperature.
According to Gay Lussac's law,
At constant volume, pressure of gas is directly proportional to its temperature.
i.e. [tex]P\propto T[/tex]
[tex]\dfrac{P}{T}=constant[/tex]..............(3)
Combining equation (1) (2) and (3)
[tex]\dfrac{PV}{T}=constant[/tex]...............(4)
Equation (4) is the combined gas law.
Or, [tex]\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}[/tex]
So, correct option is (c).