Question

Suppose 3 moles of a perfect gas held in a 4.0L container at 20.0 bar undergoes a reversible, isothermal expansion to a final pressure of 5.0 bar. How much work was done by the gas? Write down the unit in joule. (Note: the gas constant that you may need is: R=0.08314 bar L/ K mol or R = 8.3145 J/K mol; you may need both values.)

Answer 1

The work done by the perfect gas during the isothermal expansion is 34.53 kJ or 34530 J.

Step-by-step explanation:

To calculate the work done by a perfect gas during an isothermal expansion, we use the following formula for a reversible process:

w = -nRT log(ℓ P2/P1)

Giving that n = 3 moles, R = 8.3145 J/K·mol (as we will express work in joules), P1 = 20.0 bar and P2 = 5.0 bar, we first need to convert bar to Pascal (SI unit) where 1 bar = 10⁵ Pa. However, since R is given in terms of bar, we don't need to convert it. Now, we can substitute our values into the formula:

w = - (3 moles) × (8.3145 J/K·mol) × log(5.0 bar / 20.0 bar)

Upon calculation, the natural logarithm of 1/4 is -1.386, therefore the work done by the gas can be calculated as:

w = -3 × 8.3145 × -1.386 = 34.53 kJ

Therefore, the work done by the gas is 34.53 kJ, or 34530 J when expressed in joules.