Question

a chemistry grad student measures the performance z of the new pump in his lab. the result is: z = 18.7 mpa·cm³·s⁻¹
convert z to j·s⁻¹.

Explanation:

Step1: Define unit conversion factors

Recall that $1\ \text{MPa} = 10^6\ \text{Pa}$, $1\ \text{Pa} = 1\ \text{J}\cdot\text{m}^{-3}$, and $1\ \text{m}^3 = 10^6\ \text{cm}^3$.

Step2: Substitute units into Z

$$\begin{align*} Z&=18.7\ \text{MPa}\cdot\text{cm}^3\cdot\text{s}^{-1}\\ &=18.7\times10^6\ \text{Pa}\cdot\text{cm}^3\cdot\text{s}^{-1}\\ &=18.7\times10^6\ \text{J}\cdot\text{m}^{-3}\cdot\text{cm}^3\cdot\text{s}^{-1} \end{align*}$$

Step3: Convert $\text{cm}^3$ to $\text{m}^3$

Since $1\ \text{cm}^3 = 10^{-6}\ \text{m}^3$, substitute:

$$\begin{align*} Z&=18.7\times10^6\ \text{J}\cdot\text{m}^{-3}\times10^{-6}\ \text{m}^3\cdot\text{s}^{-1}\\ &=18.7\times10^6\times10^{-6}\ \text{J}\cdot\text{s}^{-1} \end{align*}$$

Step4: Simplify the expression

$$ Z=18.7\ \text{J}\cdot\text{s}^{-1} $$

Answer:

$18.7$