This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Let's re-calculate P_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: P_1 × V_1^ = P_2 × V_2^ We can rearrange this formula to solve for P_2: P_2 = P_1 × (V_1 / V_2)^ Now, let's substitute the known values: P_1 = 100 kPa V_1 = 0.082 m^3 V_2 = 0.0054 m^3 = 1.4 Step 1: Calculate the ratio of volumes. V_1 / V_2 = 0.082 m^3 / 0.0054 m^3 V_1 / V_2 ≈ 15.185 Step 2: Raise the volume ratio to the power of . (V_1 / V_2)^ = (15.185)^1.4 Let's calculate this value: (15.185)^1.4 ≈ 45.0804 Step 3: Multiply by P_1. P_2 = 100 kPa × 45.0804 P_2 ≈ 4508.04 kPa So, your calculation of P_2 = 4508.043827 kPa is correct. My previous value might have had a slight rounding difference. The pressure at state 2 is approximately 4508.04 kPa.