A heat recovery system (HRS) is used to conserve heat from the surroundings and supply it to the Mars Rover. The HRS fluid loops use Freon as the working fluid. The instrumentation must be kept as a temperature greater than −67 degrees Fahrenheit [°F] to avoid damage.

The temperature in the area of Mars where the rover is exploring is 189 kelvins [K]. If the system must remove 47.4
British Thermal Units [BTU] of energy, what volume of Freon is needed in units of liters [L]?

Some facts about Freon:
The specific heat of Freon is 74
joules per mole kelvin J/(mol °K)]
The specific gravity of Freon is 1.49
The molecular mass of Freon is 120 grams per mole [g/mol]

0.304 L of Freon is needed

Explanation:

Q = mCT

Q is quantity of energy that must be removed = 47 BTU = 47×1055.06 = 49587.82 J

C is specific heat of Freon = 74 J/mol.K = 74 J/mol.K × 1 mol/120 g = 0.617 J/g.K

T is temperature in the area of Mars = 189 K

m = Q/CT = 49587.82/(0.617×189) = 452.23 g = 452.24/1000 = 0.45223 kg

Density of Freon = specific gravity of Freon × density of water = 1.49 × 1000 kg/m^3 = 1490 kg/m^3

Volume of Freon = mass/density = 0.45223/1490 = 0.000304 m^3 = 0.000304×1000 = 0.304 L

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