The gas laws describe the behavior of gases under specific conditions of temperature, pressure, and volume. Three gas laws show the relationship between two variables when all others are held constant: Boyle’s law (pressure and volume are inversely proportional), Charles’s law (volume and temperature are directly proportional), and Gay-Lussac’s law (temperature and pressure are directly proportional).
Select the balloon volume that would represent the following conditions: the temperature is increased by half while the pressure is simultaneously decreased by half.
To find the new volume of the balloon under these conditions, we can use a combination of Charles's law and Gay-Lussac's law.
According to Charles's law, volume and temperature are directly proportional:
V1/T1 = V2/T2
Let's assume the initial volume of the balloon is V1 and the initial temperature is T1. Since the temperature is increased by half, the new temperature (T2) would be 1.5 times the initial temperature.
Next, according to Gay-Lussac's law, temperature and pressure are directly proportional:
P1/T1 = P2/T2
In this case, the pressure is decreased by half, so the new pressure (P2) would be 0.5 times the initial pressure.
Now we have V1, T1, T2, P1, and P2. We can use these values to calculate the new volume (V2) of the balloon.
(V1/T1) = (V2/T2)
V1/T1 = V2/(1.5*T1)
V2 = V1 * 1.5
(P1/T1) = (P2/T2)
P1/T1 = 0.5/T2
T2 = 2
So, the new volume of the balloon under the given conditions is 1.5 times the initial volume.