Question

Find the total translational kinetic energy of 1.5 l of oxygen gas held at a temperature of 0°c and a pressure of 0.8 atm.

Answer 1

To calculate the total translational kinetic energy of 1.5 liters of oxygen gas at 0°C and 0.8 atm, use the ideal gas law to find the number of moles and then apply the translational kinetic energy equation (KEtrans = (3/2)nRT).

Step-by-step explanation:

To find the total translational kinetic energy (KEtrans) of 1.5 liters of oxygen gas at 0°C (273 K) and 0.8 atm, we can use the ideal gas law and the equipartition theorem. The ideal gas law PV = nRT can give us the number of moles of oxygen gas when rearranged to n = PV/RT. Here, P is the pressure, V is the volume, R is the ideal gas constant, and T is the temperature.

Once the moles (n) are calculated, the translational kinetic energy per mole of a gas can be found using the equation KEtrans = (3/2)nRT, where n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. By substituting the values into the equation, we can find the total translational kinetic energy of the gas sample.

Answer 2

The ideal gas law states that:

`pV=nRT`
where
p is the gas pressure
V is its volume
n is the number of moles
R is the gas constant
T is the absolute temperature

However, this equation can be also rewritten as

`PV= (2)/(3)NK` (1)
where
N is the number of molecules in the gas, and K is the average kinetic energy of the molecules. Therefore, NK represents the total kinetic translational energy of the gas.

For the gas in our problem,

`p=0.8 atm = 8.08 \cdot 10^4 Pa`

`V=1.5 L =1.5 \cdot 10^(-3) m^3`
So, the total translational kinetic energy of the gas is (using eq.(1) )

`NK= (3)/(2)pV= (3)/(2)(8.08 \cdot 10^4 Pa)(1.5 \cdot 10^(-3) m^3)=181.8 J`