A sample of gas has a volume of 2.00 L and a pressure of 0.750 kPa when its temperature is 25°C. If the volume is expanded to 4.00 L and the pressure reduced to

0.500 kPa, what must the temperature become?

379°C

397°C

379 K

397K

The final temperature is 397 K.

Explanation:

Boyle's law relates volume and pressure by expressing:

"The volume occupied by a certain gaseous mass at constant temperature is inversely proportional to pressure"

Boyle's law is expressed mathematically as:

P * V = k

where k is a constant.

Charles's Law consists of the relationship between the volume and the temperature of a certain amount of ideal gas, which is kept at a constant pressure. This law states: "At constant pressure, the volume that a gas sample occupies is directly proportional to the temperature"

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

Finally, Gay-Lussac's law establishes the relationship between pressure and temperature of a gas when the volume is constant. This law states that the pressure of a fixed volume of a gas is directly proportional to its temperature. That is, if the volume of a certain quantity of ideal gas at moderate pressure is kept constant, the quotient between pressure and temperature remains constant.

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

Supposing you have a gas that is at a pressure P1, at a volume V1 and at a temperature T1 at the beginning of the experiment, by varying the temperature to a new value T2, then the pressure will change to P2 and the volume to V2, and will fulfill:

In this case, you have:

Replacing:

and solving you get:

T2= 397 K

The final temperature is 397 K.

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