Answer:
T2 = 169.89 K or -103.26 °C
Explanation:
In order to find out the temperature of air at a given volume of 150 cm³, let's first discuss the relationship between Volume and Temperature of an ideal gas.
What is the relationship between Volume and Temperature?
According to Jacques Alexandre Charles - a french physicist, mathematician and inventor, the volume of an ideal gas at constant pressure is directly proportional to its absolute temperature. Absolute temperature is measure by Kelvin unit.
It means that as Volume increases, Temperature also increases at constant temperature
It can also be written as such:
At constant P:
=
where:
V1 - initial volume
V2 - final volume
T1 - initial temperature
T2 - final temperature
** T is measured in Kelvin.
Now that we have already discussed the relationship between Volume and Temperature, we can now answer the given problem:
Lets list down the given facts:
V1 = 250 cm³
T1 = 10 °C
V2 = 150 cm³
Required:
T2 = ?
IMPORTANT:
Before we equate the given into Charle's Law equation, we should always convert the temperature into Kelvin if the unit used for measuring the temperature is °C
Hence,
T1 = 10°C + 273.15 = 283.15 K
T1 = 283.15 K
Solution:
Let us now equate the given into Charle's Law equation:
=
Since we are finding T2, I will equate the above equation to T2.
T2 =
T2 = → In this part the unit for volume will be cancelled out.
Thus,
T2 = 169.89 K
We can then convert the above to °C
T2 = 169.89 - 273.15 = -103.26 °C
Thus,
The temperature of air at a volume of 150 cm³ is -103.26 °C.
CTTO <3
