Question

Find the total translational kinetic energy of
3 L of oxygen gas held at a temperature of
−3C◦ and a pressure of 2 atm.
Answer in units of J.

Answer 1

Solution:

For every degree of freedom of the molecule gas has the same average energy

$$\varepsilon_i=\frac {1}{2} kT$$

where k is the Boltzmann constant, T is the thermodynamic temperature of the gas. The translational motion of a diatomic oxygen molecule corresponds to three degrees of freedom, and rotational - two. Then the average kinetic energy of the molecule

$$\varepsilon = \frac {5}{2} kT$$

The kinetic energy of motion of all gas molecules

$$E=N \varepsilon$$

The number of all gas molecules N, concentration of molecules n

$$p=nkT$$

$$n=\frac {N}{V}$$

$$N= \frac {pV}{kT}$$

$$E= N \times \frac {5}{2} kT$$

$$E= \frac {pV}{kT}\times \frac {5}{2} kT$$

$$E= \frac {5}{2} pV$$

$p=2\times 101325.011 \frac {N}{m^2}= 2.03 \times 10^5 \frac {N}{m^2}$

$V=3\times 10^{-3} m^3$

$$E=1.5\times 10^3 J$$

Answer: $1.5\times 10^3 J$