Question

a nasa spacecraft measures the rate ( r ) at which atmospheric pressure on mars decreases with altitude. the result at a certain altitude is ( r = 0.0752 space \text{kpa·km}^{-1} ). convert ( r ) to ( \text{kj·m}^{-4} ).

Explanation:

Step1: Recall unit conversion factors

$1\ \text{kPa} = 1\ \text{kJ·m}^{-3}$, $1\ \text{km} = 1000\ \text{m}$ so $1\ \text{km}^{-1} = 10^{-3}\ \text{m}^{-1}$

Step2: Substitute units into R

$R = 0.0752\ \text{kPa·km}^{-1} = 0.0752\ \text{kJ·m}^{-3} \times 10^{-3}\ \text{m}^{-1}$

Step3: Calculate the final value

$R = 0.0752 \times 10^{-3}\ \text{kJ·m}^{-4} = 7.52 \times 10^{-5}\ \text{kJ·m}^{-4}$

Answer:

$7.52 \times 10^{-5}$