Consider a perfect gas that occupies 2.5 dm3 at a pressure of 3.00 bar. The gas is compressed at a constant pressure pex, so that the final volume is 0.5 dm3. The final temperature is the same as in the beginning, although it can change along the path. Calculate pex in bar. (b) What is the work involved with the pressure you calculated in part-a in joules.

a) Pex = 15 bar

b) work = 3000 J

Explanation:

Step 1: Data given

Volume of the gas = 2.5 dm³

Pressure of the gas = 3.00 bar

The gas is compressed at a constant pressure pex, so that the final volume is 0.5 dm³

The final temperature is the same as in the beginning.

Step 2: Calculate Pex

If the gas is compressed isothermally (=constant temperature), then via the ideal gas law we can write:

P2 = Pex = (P1*V1) / V2

Pex = (3 * 2.5) / 0.5

Pex = 15 bar

Step 3: Calculate the work

If Pex is constant, then is:

w = - ∫Pex * dV = - Pex * ΔV = - 15 * (0.5-2.5) dm³ = 30dm³ bar

30dm³ bar * 10^5 Pa / bar * 0.1³ m³/dm³ = 3000 kg*m²/s² = 3000 J