Order the follow processes from (1) the least work done by the system to (5) the most work done by one mole of an ideal gas at 25°c. 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.

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 :

The formula used for isothermally irreversible expansion is :

where,

w = work done

= external pressure

= initial volume of gas

= final volume of gas

The expression used for work done in reversible isothermal expansion will be,

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)