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       $R  = 0.0498 *10^{-3} \frac{kJ}{m^4}$

Explanation:

From the question we are told that

   The altitude is  $R = 0.0498 \ kPAkm^{-1}$

Generally  

     $1 k PA  =  1000 PA$

So  

   $R = 0.0498 \frac{1000PA}{ km}$

Also  

   1 km  =  1000 m

   

So  

     $R = 0.0498 \frac{1000PA}{ 1000m}$

=>   $R = 0.0498 \frac{1 PA}{ 1 m}$

Now  PA  is Pascal which is mathematically represented as

       $PA =  \frac{N}{m^2 }$

So

   $R  = 0.0498 \frac{\frac{N}{m^2} }{m}$

    $R  = 0.0498 \frac{N}{m^3}$

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

      $J =  N  *  m$

So  

  $R  = 0.0498 \frac{ N \frac{m}{m} }{m^3}$

=>  $R  = 0.0498 \frac{\frac{J}{m} }{m^3}$

=>  $R  = 0.0498 \frac{J}{m^4}$

Generally  

      $1 J \to 1.0*10^{-3} kJ$

      $0.0498 J  \to x kJ$

=>      $x =  \frac{0.0498 *  1.0*10^{-3}}{1}$

=>   $0.0498 *10^{-3} kJ$

So

    $R  = 0.0498 *10^{-3} \frac{kJ}{m^4}$