You want to heat 1 kg of water 10 celsius and you have the following methods under consideration. The heat capacity of water is 4.184 J/K g.
(a)You can send the water through a solar collector that has an area of 1 m^2. How long will it take if the sun's intensity on the collector is 4 J/min cm^2?
(b)You can make a charcoal fire. The heat of combustion of graphite is -393 kJ/mol. How much charcoal will have to burn?
How much heat to you need? That's
q = mass H2O x specific heat H2O x delta T.
q = 1000 x 4.184 x 10 = 41840 J
a. (4J/min*cm^2) x (100 cm/1 m) x (100 cm/1m) x # min = 41840. Solve for # min
b. C + O2 ==> CO2 + 393,000 J
(393,000/12 g C) x #g C = 393,000
Solve for #g C
To calculate the time required to heat 1 kg of water by 10 degrees Celsius using a solar collector, we need to consider the heat input from the collector and the heat capacity of water.
(a) Using a solar collector:
1. Calculate the heat energy required to raise the temperature of 1 kg of water by 10 degrees Celsius:
Heat Energy (Q) = mass * specific heat capacity * temperature change
Q = 1 kg * 4.184 J/K g * 10 K
Q = 41.84 kJ
2. Calculate the energy received by the solar collector:
Energy received = intensity * area * time
The intensity is given as 4 J/min cm^2, and the area is 1 m^2.
Convert the intensity unit from J/min cm^2 to J/s m^2:
4 J/min cm^2 * (1 min/60 s) * (100 cm/1 m)^2 = 6.67 J/s m^2
Equate the energy received by the collector to the heat energy required:
Energy received = Heat Energy (Q)
6.67 J/s m^2 * 1 m^2 * time = 41.84 kJ
Simplify and solve for time:
time = 41.84 kJ / (6.67 J/s m^2)
time ≈ 627.19 seconds or 10.46 minutes
Therefore, it will take approximately 10.46 minutes to heat 1 kg of water by 10 degrees Celsius using a solar collector.
(b) Using a charcoal fire:
1. Calculate the heat energy required to raise the temperature of 1 kg of water by 10 degrees Celsius (as calculated in part (a)). This value is 41.84 kJ.
2. Calculate the amount of heat released by the combustion of charcoal:
The heat of combustion of graphite (charcoal) is given as -393 kJ/mol.
Convert kJ to J:
-393 kJ = -393,000 J/mol
Calculate the number of moles of graphite required to release the heat energy of 41.84 kJ:
moles of graphite = heat energy / heat of combustion
moles of graphite = 41.84 kJ / (-393,000 J/mol)
Since 1 mole of carbon (graphite) has a molar mass of 12.01 g/mol, we can calculate the mass of charcoal required:
mass of charcoal = moles of graphite * molar mass of carbon
mass of charcoal = (41.84 kJ / (-393,000 J/mol)) * 12.01 g/mol
Simplify and solve for mass of charcoal:
mass of charcoal ≈ -0.00637 grams
Note: The negative sign indicates that the heat of combustion is released from the charcoal.
Therefore, you would need approximately 0.00637 grams of charcoal to burn in order to provide the heat energy required to heat 1 kg of water by 10 degrees Celsius.