Final answer:
To convert Z from MPa·cm³·s⁻¹ to J·s⁻¹, multiply Z by 10^6 Pa·m³·s⁻¹. To convert Z to kJ/s, divide Z by 1,000. The performance Z of the pump is 9.5 J*s⁻¹, which is also equivalent to 0.0095 kJ/s after applying the unit conversion from MPa*cm³*s⁻¹ to J*s⁻¹ and then to kJ/s.
Step-by-step explanation:
To convert Z from MPa·cm³·s⁻¹ to J·s⁻¹, we need to take into consideration the units of each component. 1 MPa is equal to 1,000,000 Pa. 1 cm³ is equal to 10⁻⁶ m³. Therefore, we can convert Z to J·s⁻¹ as follows:
Z (J·s⁻¹) = Z (MPa·cm³·s⁻¹) × (10⁶ Pa/MPa) × (10⁻⁶ m³/cm³) = Z × 10 Pa·m³·s⁻¹
To convert Z to kJ/s, we divide Z by 1,000 to convert from J to kJ. Therefore, Z (kJ/s) = Z (J·s⁻¹) ÷ 1,000.
The performance Z of the pump is 9.5 J*s⁻¹, which is also equivalent to 0.0095 kJ/s after applying the unit conversion from MPa*cm³*s⁻¹ to J*s⁻¹ and then to kJ/s.
The student is looking to convert the unit of performance, Z, of a new pump measured in MPa*cm³*s⁻¹, to units of J*s⁻¹ and kJ/s. The conversion is based on the fact that a megapascal (MPa) multiplied by cubic centimeters (cm³) is equivalent to the SI unit for work or energy, which is a joule (J). Therefore, to convert 9.5 MPa*cm³*s⁻¹ to J*s⁻¹, we multiply by the conversion factor for MPa to pascals and cm³ to cubic meters:
Z = 9.5 MPa*cm³*s⁻¹
Z = 9.5 x 10¶ Pa * 9.5 x 10⁻¶ m³ * s⁻¹
Z = 9.5 x 1 J*s⁻¹ = 9.5 J*s⁻¹
Now, to convert this to kJ/s, we move the decimal point three places to the left:
Z = 9.5 J*s⁻¹ / 1000 = 0.0095 kJ/s
Thus, the performance Z of the pump in different units is 9.5 J*s⁻¹ or 0.0095 kJ/s.