Final answer:
To find the final pressure when the volume is compressed to 0.125 m³ in the given relation PV^1.25 = C, we can use the equation and calculate the value of C. By dividing the value of C by the new volume, we can find the final pressure. The final pressure is approximately 181 kN/m².
Step-by-step explanation:
To solve the problem, we can use the equation PV^1.25 = C. We are given the initial pressure P1 = 140 kN/m² and the initial volume V1 = 0.15 m³. We need to find the final pressure when the volume is compressed to 0.125 m³. Using the equation, we can set up the following equation:
140 * (0.15)^1.25 = C
To find C, we can plug in the values.
C = 140 * (0.15)^1.25 = 140 * 0.180123 = 25.21644
Now we can use the value of C to find the final pressure.
Final pressure * (0.125)^1.25 = 25.21644
Dividing both sides of the equation by (0.125)^1.25, we get:
Final pressure = 25.21644 / (0.125)^1.25 = 180.9371 kN/m².
Therefore, the final pressure when the volume is compressed to 0.125 m³ is approximately 181 kN/m² (option c).