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Answer : The order of process from (1) the least work done by the system to (5) the most work done by the system will be:
(1) < (5) < (3) < (4) < (2)
Explanation :
<u>The formula used for isothermally irreversible expansion is :</u>
where,
w = work done
= external pressure
= initial volume of gas
= final volume of gas
<u>The expression used for work done in reversible isothermal expansion will be,</u>
where,
w = work done = ?
n = number of moles of gas = 1 mole
R = gas constant = 8.314 J/mole K
T = temperature of gas =
= initial volume of gas
= final volume of gas
First we have to determine the work done for the following process.
(1) An isothermal expansion from 1 L to 10 L at an external pressure of 2.5 atm.
(2) A free isothermal expansion from 1 L to 100 L.
(3) A reversible isothermal expansion from 0.5 L to 4 L.
(4) A reversible isothermal expansion from 0.5 L to 40 L.
(5) An isothermal expansion from 1 L to 100 L at an external pressure of 0.5 atm.
Thus, the order of process from (1) the least work done by the system to (5) the most work done by the system will be:
(1) < (5) < (3) < (4) < (2)
Answer:
In the kinetic molecular theory, the molecules of an ideal gas are in constant random motion inside the container of the gas, and the pressure of the gas (which is the pressure exerted by the molecules in their collisions with the walls of the container) arise from this random motion of the molecules.
The main assumptions of the kinetic theory of gases are:
- The gas consists of a large number of molecules that collide between each other and the walls of the container; all these collisions are elastic
- The duration of the collisions is negligible compared to the time between the collisions
- The number of molecules is so large that statistics can be applied
- Intermolecular forces between the molecules are negligible (except during the collisions)
- The volume of the molecules is negligible compared to the volume of the container
In particular, the pressure of the gas is directly proportional to the average kinetic energy of the molecules, according to the equation:
where
p is the pressure of the gas
V is the volume of the container
K is the average kinetic energy of the molecules in the gas
We see that as the pressure is higher, the higher the kinetic energy of the particles: this means that the molecules will move faster, on average.
Therefore in this problem, the gas that exerts a pressure of 1.5 atm will have molecules moving faster than the molecules of the gas exerting a pressure of only 1.0 atm.