Question

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]

Answer 1

Answer:

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