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otez555 [7]
3 years ago
10

A spacecraft is fueled using hydrazine (N2H4; molecular weight of 32 grams per mole [g/mol]) and carries 1640 kilograms [kg] of

fuel. On a mission to orbit a planet, the fuel will first be warmed from −186 degrees Fahrenheit [°F] to 78 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 300 watts [W] of power available to heat the fuel, how long will the heating process take in units of hours [h]?
Physics
1 answer:
Sauron [17]3 years ago
6 0

Answer:

The value is t = 689.029 \  hours

Explanation:

From the question we are told that

The molar mass of hydrazine is Z =  32 g/mol = \frac{32}{1000} = 0.032 \  kg/mol

The initial temperature is T_i  =  -186 ^o F = (-186-32) *\frac{5}{9} +273.15 = 152\ K

The final temperature is T_f  =  78 ^o F = (78-32) *\frac{5}{9} +273.15 = 298.7 \ K

The specific heat capacity is c_h  =  0.099 [kJ/(mol K)] = 0.099 *10^3 J/(mol/K)

The power available is P = 300 \ W

The mass of the fuel is m =   1640 \  kg

Generally the number of moles of hydrazine present is

n  =  \frac{m}{Z}

=> n  =  \frac{1640}{= 0.032}

=> n  =  51250 \ mol

Generally the quantity of heat energy needed is mathematically represented as

Q =  n * c_h * (T_f -T_i)

=> Q =  51250  * 0.099 *10^3  * (298.7 - 152)

=> Q =  7.441516913 * 10^{8} \  J

Generally the time taken is mathematically represented as

t =  \frac{Q}{P}

=> t =  \frac{7.441516913 * 10^{8} }{300}

=> t = 2480505.6377 s

Converting to hours

t = \frac{2480505.6377}{3600}

=> t = 689.029 \  hours

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