Question

If the pressure acting on a given sample of an ideal gas at constant temperature is tripled, what happens to the volume of the gas? a)The volume is reduced to one-third of its original value. b)The volume is reduced to one-ninth of its original value. c) The volume remains constant. d)The volume is increased by a factor of three times its original value. e) The volume is increased by a factor of nine times its original value.

Answer 1

Answer:

a)The volume is reduced to one-third of its original value.

Explanation:

For a gas at constant temperature, we can apply Boyle's law, which states that the product between pressure and volume is constant:

$pV=const.$

where p is the pressure and V the volume.

In our case, this law can also be rewritten as

$p_1 V_1 = p_2 V_2$

where the labels 1 and 2 refer to the initial and final conditions of the gas.

For the gas in the problem, the pressure of the gas is tripled, so

$p_2 = 3p_1$

And re-arranging the equation we find what happens to the volume:

$V_2 = \frac{p_1 V_1}{p_2}=\frac{p_1 V_1}{3p_1}=\frac{V_1}{3}$

so, the volume is reduced to 1/3 of its original value.