Question

a chemistry grad student measures the performance z of the new pump in his lab. the result is: z = 9.4 kpa·mm³·s⁻¹. convert z to mj·s⁻¹.

Explanation:

Step1: Recall unit conversion factors

$1\ \text{kPa} = 1000\ \text{Pa}$, $1\ \text{mm}^3 = 10^{-9}\ \text{m}^3$, $1\ \text{J} = 1\ \text{Pa·m}^3$, $1\ \text{mJ} = 10^{-3}\ \text{J}$

Step2: Convert kPa to Pa and mm³ to m³

$9.4\ \text{kPa·mm}^3·\text{s}^{-1} = 9.4 \times 1000\ \text{Pa} \times 10^{-9}\ \text{m}^3·\text{s}^{-1}$

Step3: Calculate Pa·m³ to J

$9.4 \times 1000 \times 10^{-9}\ \text{Pa·m}^3·\text{s}^{-1} = 9.4 \times 10^{-6}\ \text{J·s}^{-1}$

Step4: Convert J to mJ

$9.4 \times 10^{-6}\ \text{J·s}^{-1} = 9.4 \times 10^{-3}\ \text{mJ·s}^{-1}$

Answer:

$9.4 \times 10^{-3}$