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

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

Step-by-step 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 = (p_1 V_1)/(p_2)=(p_1 V_1)/(3p_1)=(V_1)/(3)`

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