A gas occupies a volume of 10cm3 at 100kPa. If the pressure is increased to 200kPa, What is the new volume if the temperature remains constant at 27°C.
Dr Bob showed you how to do these in two problems below.
The only thing I might add is remember that you need to use degrees Kelvin in your P V = n R T calculations which is degrees Centigrade + 273
P1 V1/T1 = P2 V2/T2
Here T is constant so
P1 V1 = P2 V2
To determine the new volume of the gas, we can use Boyle's law, which states that the pressure and volume of a gas are inversely proportional when the temperature is constant. Boyle's law can be expressed as:
P1*V1 = P2*V2
Where:
P1 = initial pressure
V1 = initial volume
P2 = final pressure
V2 = final volume
Given:
P1 = 100 kPa
V1 = 10 cm³
P2 = 200 kPa
T = 27 °C = 300 K (since temperature needs to be in Kelvin for calculations)
Let's solve for V2:
P1*V1 = P2*V2
(100 kPa) * (10 cm³) = (200 kPa) * V2
(100 kPa * cm³) = (200 kPa) * V2
Now, let's cancel the units of pressure:
(100 cm³) = (200) * V2
To isolate V2, divide both sides by 200:
V2 = (100 cm³) / (200)
V2 = 0.5 cm³
Therefore, the new volume of the gas, when the pressure is increased to 200 kPa and the temperature remains constant at 27 °C, is 0.5 cm³.
To find the new volume of the gas when the pressure is increased, we can use the relationship between pressure and volume known as Boyle's Law. Boyle's Law states that the pressure and volume of a gas are inversely proportional, assuming the temperature remains constant.
The formula for Boyle's Law is:
P1V1 = P2V2
where P1 is the initial pressure, V1 is the initial volume, P2 is the final pressure, and V2 is the final volume.
In this case, we are given that the initial volume (V1) is 10 cm3 and the initial pressure (P1) is 100 kPa. The final pressure (P2) is given as 200 kPa.
Since the temperature remains constant, we can rewrite the formula as:
P1V1 = P2V2
Substituting the given values:
(100 kPa)(10 cm3) = (200 kPa)(V2)
Simplifying the equation:
1000 cm3 kPa = 200V2 cm3 kPa
Dividing both sides of the equation by 200 kPa:
5 cm3 = V2
Therefore, the new volume of the gas when the pressure is increased to 200 kPa while the temperature remains constant at 27°C is 5 cm3.