# Combined gas law

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### Combined Gas Law

The Combined Gas Law can be derived by
multiplying Boyle's law by the
laws of Charles and Gay-Lussac.

**P**_{1}V_{1} = P_{2}V_{2}

P_{1}V_{1}^{2} / T_{1} = P_{2}V_{2}^{2}
/ T_{2}

P_{1}^{2}V_{1}^{2} / T_{1}^{2}
= P_{2}^{2}V_{2}^{2} / T_{2}^{2}

By taking the square root of this result we get the combined gas law:

**P**_{1}V_{1} / T_{1} = P_{2}V_{2}
/ T_{2}

# Combined
gas law

A sample of gas has an initial volume of 2dm^{3} (V_{1})
at a temperature of 300 K(T_{1}) and a pressure of 1atm (P_{1}).
If the gas is compressed to a volume of 0.5dm^{3}(V_{2})and
heated to 350 K(T_{2}) what is the final pressure (P_{2})?

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