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A gas expands from 50 m3 to 58 m3 at a constant pressure of 105 Nm⁻². Calculate the work done by the gas.

Physics

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Step-by-step solution

3 steps
  1. Identify the given values.

    Initial volume (V1V_1) = 50 m350 \, \text{m}^3
    Final volume (V2V_2) = 58 m358 \, \text{m}^3
    Constant pressure (PP) = 105 Nm−210^5 \, \text{Nm}^{-2}

  2. Calculate the change in volume (ΔV\Delta V).

    The change in volume is the final volume minus the initial volume.

    ΔV=V2−V1\Delta V = V_2 - V_1 ΔV=58 m3−50 m3\Delta V = 58 \, \text{m}^3 - 50 \, \text{m}^3 ΔV=8 m3\Delta V = 8 \, \text{m}^3
  3. Calculate the work done (WW) by the gas.

    For expansion at constant pressure, the work done by the gas is given by the formula:

    W=PΔVW = P \Delta V

    Substitute the values of pressure and change in volume:

    W=(105 Nm−2)×(8 m3)W = (10^5 \, \text{Nm}^{-2}) \times (8 \, \text{m}^3) W=8×105 N⋅mW = 8 \times 10^5 \, \text{N} \cdot \text{m}

    Since 1 N⋅m=1 J1 \, \text{N} \cdot \text{m} = 1 \, \text{J} (Joule),

    W=8×105 JW = 8 \times 10^5 \, \text{J}

    Comparing this result with the given options, it matches option D.

    The work done by the gas is \boxed{\text{8 \times 10^5 J}}.

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