Question

A NASA spacecraft measures the rate of at which atmospheric pressure on Mars decreases with altitude. The result at a certain altitude is:

Answer 1

Complete 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 \ kPAkm^(-1)` Convert R to
`kJ*m^(-4)`

Answer:

The value is
`R  = 0.0498 *10^(-3) (kJ)/(m^4)`

Step-by-step explanation:

From the question we are told that

The altitude is
`R = 0.0498 \ kPAkm^(-1)`

Generally

`1 k PA  =  1000 PA`

So

`R = 0.0498 (1000PA)/( km)`

Also

1 km = 1000 m

So

`R = 0.0498 (1000PA)/( 1000m)`

=>
`R = 0.0498 (1 PA)/( 1 m)`

Now PA is Pascal which is mathematically represented as

`PA =  (N)/(m^2 )`

So

`R  = 0.0498 ((N)/(m^2) )/(m)`

`R  = 0.0498 (N)/(m^3)`

Looking the unit we are arrive at we see that it contains J which is mathematically represented as

`J =  N  *  m`

So

`R  = 0.0498 ( N (m)/(m) )/(m^3)`

=>
`R  = 0.0498 ((J)/(m) )/(m^3)`

=>
`R  = 0.0498 (J)/(m^4)`

Generally

`1 J \to 1.0*10^(-3) kJ`

`0.0498 J  \to x kJ`

=>
`x =  (0.0498 *  1.0*10^(-3))/(1)`

=>
`0.0498 *10^(-3) kJ`

So

`R  = 0.0498 *10^(-3) (kJ)/(m^4)`