A fixed mass of an ideal gas has a volume of 800 cm3 under certain conditions. The pressure (in kPa) and temperature (in K) are both doubled. What is the volume of the gas after these changes with other conditions remaining the same

Gay-Lussac's law states that the pressure of a gas is directly proportional to its temperature: increasing the temperature will turn off the pressure, while decreasing the temperature will decrease the pressure.

This law can be expressed mathematically as follows:

[tex]\frac{P}{T}=k[/tex]

Boyle's law

Boyle's law states that the volume occupied by a given mass of gas at constant temperature is inversely proportional to the pressure.

Boyle's law is expressed mathematically as:

P×V=k

Charles's Law

Finally, Charles's Law consists of the relationship that exists between the volume and the temperature of a certain amount of ideal gas, which is maintained at a constant pressure.

This law states that the volume is directly proportional to the temperature of the gas: if the temperature increases, the volume of the gas increases, while if the temperature of the gas decreases, the volume decreases.

In summary, Charles' law is a law that says that when the amount of gas and pressure are kept constant, the ratio between volume and temperature will always have the same value:

[tex]\frac{V}{T}=k[/tex]

Combined law equation

Combined law equation is the combination of three gas laws called Boyle's, Charlie's and Gay-Lusac's law:

[tex]\frac{PxV}{T}=k[/tex]

Studying two states, one initial 1 and the other final 2, it is fulfilled:

[tex]\frac{P1xV1}{T1}=\frac{P2xV2}{T2}[/tex]

Volume of the gas after the changes

In this case, you know:

V1= 800 cm³
P2= 2× P1
T2= 2× T1

Replacing in Combined law equation:

[tex]\frac{P1x800 cm^{3} }{T1}=\frac{2x P1xV2}{2 xT1}[/tex]

Solving:

[tex]V2=\frac{P1x800 cm^{3} }{T1}\frac{2x T1}{2 xP1}[/tex]

V2= 800 cm³

Finally, the volume of the gas after these changes with other conditions remaining the same is 800 cm³.

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