What is the temperature of a 100 liter container having 1 mole of an ideal gas at a pressure of 20 kilopascals?
To find the temperature of a container with a given volume, pressure, and number of moles of an ideal gas, you can use the ideal gas law equation:
PV = nRT
Where:
P: pressure (in pascals)
V: volume (in cubic meters)
n: number of moles
R: ideal gas constant (8.31 J/(mol·K))
T: temperature (in Kelvin)
First, convert the volume from 100 liters to cubic meters:
1 liter = 0.001 cubic meters
So, 100 liters = 100 * 0.001 = 0.1 cubic meters
Since the pressure is given in kilopascals, convert it to pascals:
1 kilopascal = 1000 pascals
So, 20 kilopascals = 20 * 1000 = 20,000 pascals
Now, rearrange the ideal gas law equation to solve for temperature:
T = PV / nR
Plug in the values:
P = 20,000 pascals
V = 0.1 cubic meters
n = 1 mole
R = 8.31 J/(mol·K)
T = (20,000 * 0.1) / (1 * 8.31)
Calculate:
T = 20,000 / 8.31
T ≈ 2406.3 Kelvin
So, the temperature of the 100 liter container with 1 mole of ideal gas at a pressure of 20 kilopascals is approximately 2406.3 Kelvin.