Derived from Byle's Law and Charles' Law

Return to Combined Ga Law: Ten Examples

**Discussion:** (a) Charles' Law is the change in volume with respect to temperature __for constant pressure__ while (b) Boyle's law is the change in volume with respect to pressure __for constant temperature__. When you combine the two laws, you must account for these two points.

**Solution:**

1) Assume we have a gas sample present at the following values:

pressure = P_{1}

volume = V_{1}

temperature = T_{1}

2) We now allow the gas to change, at constant temperature, to the following state:

pressure = P_{2}

volume = V_{*}

temperature = T_{1}

3) By Boyle's Law, we know the following to then be true:

P_{1}V_{1}= P_{2}V_{*}<--- no T value since it is constant

4) Keeping the pressure constant, we allow the gas to move to the following state:

pressure = P_{2}

volume = V_{2}

temperature = T_{2}

5) By Charles' Law, we know the following to be true:

V _{*}V _{2}–––– = –––– <--- no P value since pressure is constant T _{1}T _{2}

6) Isolate V_{*} in each expression:

P _{1}V_{1}V _{*}=–––– P _{2}

T _{1}V_{2}V _{*}=–––– T _{2}

7) Since, V_{*} = V_{*}, we can write this:

P _{1}V_{1}T _{1}V_{2}–––– = –––– P _{2}T _{2}

8) Multiplying each side by the factor P_{2} / T_{1} yields the most-widely used form of the combined gas law:

P _{1}V_{1}P _{2}V_{2}–––– = –––– T _{1}T _{2}