A gas is heated while being kept at
a constant pressure. If its temperature in kelvins
increases by a factor of two, by what factor does the volume of the gas change?
The question asks us how the volume
of a gas changes when we increase the temperature by a specific amount. To answer this question, Let’s
recall Charles’s law. The volume of a fixed amount of an
ideal gas is directly proportional to its absolute temperature if the gas is kept at
a constant pressure.
Now, we’re told in the question
that the gas is kept at a constant pressure. Therefore, it follows the condition
for Charles’s law to be applicable here. This means that if we change the
temperature 𝑇 of our gas, the volume 𝑉 must change proportionally. What that means is that if we
change one of these quantities by some factor, the other would change by the same
In this question, we’ve been told
that the temperature of the gas, in kelvins, increases by a factor of two. Due to this direct proportionality
relationship, the volume of the gas must therefore also increase by a factor of
two. Hence, our final answer is that the
volume of the gas increases by a factor of two.