What is the total kinetic energy of 0.5 mol of an ideal monatomic gas confined at 8dm³ at 200kpa?
To calculate the total kinetic energy of a monatomic gas, we need to use the formula:
KE = (3/2) * n * R * T
where KE is the total kinetic energy, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
First, let's determine the value of the ideal gas constant, R. The value of R depends on the unit of pressure used. In this case, the pressure is given in kPa, so we'll use the value of R in kPa·dm³/(mol·K), which is 8.314.
Now, let's convert the volume from dm³ to m³. There are 1000 dm³ in 1 m³, so the volume is 8 dm³ converted to m³ is 0.008 m³.
Next, we'll convert the pressure from kPa to Pa. There are 1000 Pa in 1 kPa, so the pressure is 200 kPa converted to Pa is 200,000 Pa.
Finally, let's convert the temperature from degrees Celsius to Kelvin. To convert Celsius to Kelvin, we add 273.15. So the temperature of 200 K will be (200 + 273.15) K = 473.15 K.
Now we have all the necessary values to substitute into the formula:
KE = (3/2) * n * R * T
KE = (3/2) * 0.5 * 8.314 * 0.008 * 473.15
Now we can calculate the total kinetic energy.