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Question: Two moles of an ideal gas is expanded isothermally from a volume of 300 $cm^3$ to 2.5 $dm^3$ at 298 ...

Two moles of an ideal gas is expanded isothermally from a volume of 300 cm3cm^3 to 2.5 dm3dm^3 at 298 K against a constant pressure at 1.9 bar. Calculate the work done in joules.

A

-418 J

B

-565 J

C

-918 J

D

-950 J

Answer

-418 J

Explanation

Solution

  1. Convert units:

    • Vi=300 cm3=300×10−6=0.0003 m3V_i = 300\ \text{cm}^3 = 300 \times 10^{-6} = 0.0003\ \text{m}^3

    • Vf=2.5 dm3=2.5×10−3=0.0025 m3V_f = 2.5\ \text{dm}^3 = 2.5 \times 10^{-3} = 0.0025\ \text{m}^3

    • Change in volume:

      ΔV=Vf−Vi=0.0025−0.0003=0.0022 m3\Delta V = V_f - V_i = 0.0025 - 0.0003 = 0.0022\ \text{m}^3

    • Pressure:

      P=1.9 bar=1.9×105 PaP = 1.9\ \text{bar} = 1.9 \times 10^5\ \text{Pa}

  2. Calculate work done:

    • For expansion against constant external pressure, W=−PΔV=−(1.9×105)×(0.0022)=−418 JW = -P \Delta V = -\left(1.9 \times 10^5\right) \times (0.0022) = -418\ \text{J}