Why is my p2 not the same as yours mine is P2=4508.043827

Mathematics

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Step-by-step solution

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Let's re-calculate P2P_2 to ensure accuracy.

The process from state 1 to state 2 is adiabatic. For an adiabatic process, the relationship between pressure and volume is given by:
P1×V1γ=P2×V2γP_1 \times V_1^\gamma = P_2 \times V_2^\gamma

We can rearrange this formula to solve for P2P_2:
P2=P1×(V1/V2)γP_2 = P_1 \times (V_1 / V_2)^\gamma

Now, let's substitute the known values:
P1=100 kPaP_1 = 100 \text{ kPa}
V1=0.082 m3V_1 = 0.082 \text{ m}^3
V2=0.0054 m3V_2 = 0.0054 \text{ m}^3
γ=1.4\gamma = 1.4

  1. Calculate the ratio of volumes.

    V1/V2=0.082 m3/0.0054 m3V_1 / V_2 = 0.082 \text{ m}^3 / 0.0054 \text{ m}^3
    V1/V2≈15.185V_1 / V_2 \approx 15.185

  2. Raise the volume ratio to the power of γ\gamma.

    (V1/V2)γ=(15.185)1.4(V_1 / V_2)^\gamma = (15.185)^{1.4}

    Let's calculate this value:
    (15.185)1.4≈45.0804(15.185)^{1.4} \approx 45.0804

  3. Multiply by P1P_1.

    P2=100 kPa×45.0804P_2 = 100 \text{ kPa} \times 45.0804
    P2≈4508.04 kPaP_2 \approx 4508.04 \text{ kPa}

    So, your calculation of P2=4508.043827 kPaP_2 = 4508.043827 \text{ kPa} is correct. My previous value might have had a slight rounding difference.

    The pressure at state 2 is approximately 4508.04 kPa.

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