Question

A spacecraft is fueled using hydrazine ​(N2H4​; molecular weight of 32 grams per mole​ [g/mol]) and carries 1,648 kilograms​ [kg] of fuel. On a mission to orbit a​ planet, the fuel will first be warmed from negative −176 degrees Fahrenheit​ [°F] to 87 degrees Fahrenheit​ [°F] before being used after the long space flight to reach the planet. The specific heat capacity of hydrazine is 0.099 kilojoules per mole kelvin​ [kJ/(mol K)]. If there is 500watts​ [W] of power available to heat the​ fuel, how long will the heating process take in units of hours​ [h]?

Answer 1

Firstly we have heat gain relation

where

and power consumption relation

  

Now first determining the temperature in kelvin as heat capacity in kelvin

T (kelvin) = (T(Fahrenheit) + 459.67) * (5/9)

So

T1 = 157.59 K

T2 = 303.71 K

so we have

Now determining the no of moles

  

So we have

Joules

and which gives

seconds

   hours

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