Question

question 12 (1 point)
what will happen to the pressure of a gas if its absolute temperature triples (increases by a factor of three), while the number of moles of gas and the volume are held constant?
the pressure will be cut in half (decrease by a factor of two).
the pressure will double (increase by a factor of two).
the pressure will decrease by a factor of three.
the pressure will triple (increase by a factor of three).

Explanation:

Step1: Recall the ideal gas law

$$PV = nRT$$
where \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles, \(R\) is the ideal gas constant, and \(T\) is absolute temperature.

Step2: Rearrange for pressure

$$P=\frac{nR}{V}T$$

Step3: Analyze the change

Since \(n\), \(R\), and \(V\) are constant, \(P\propto T\). If \(T\) triples (\(T_{new}=3T_{old}\)), then \(P_{new}=\frac{nR}{V}(3T_{old}) = 3P_{old}\). So the pressure triples.

Answer:

The pressure will triple (increase by a factor of three).