Question

A NASA spacecraft measures the rate R of at which atmospheric pressure on Mars decreases with altitude. The result at a certain altitude is: R = 0.0498 kPA*km^-1. Convert R to kJ*m^-4

Answer 1

`R = 0.0000498 (KJ)/( m m^3)=0.0000498 (KJ)/(m^4)=4.98x10^(-5)(KJ)/(m^4)`

Explanation:

For this case we have the following value:

`R = 0.0498 (Kpa)/(Km)`

We can convert this first to
`(Kpa)/(m)` like this:

`R=0.0498 (Kpa)/(Km) *(1km)/(1000m)=0.0000498 (Kpa)/(m)`

Now we use the fact the the pressure is defined as
`P =(F)/(A)`, whre P is the pressure, F the force and A the area, so then
`Kpa= (KN)/(m^2)` and then we can replace this:

`R=0.0000498 (KN)/(m^3)`

Now from definition of work we know that
`W= Fd` where W is the work, F the force and d the distance, so then is equivalent
`KN =(KJ)/(m)`

And if we replace this into the equation we got:

`R = 0.0000498 (KJ)/( m m^3)=0.0000498 (KJ)/(m^4)=4.98x10^(-5)(KJ)/(m^4)`