How many gallons of C6H12 , measured at 20 degrees Celsius, must be burned to provide enough heat to warm 26.4m3 of water from 17.4 degrees Celsius to 32.8 degrees Celsious , assuming that all the heat of combustion is transferred to the water, which has a specific heat of 4.18 J/ (g of Degrees Celsious)?
To determine the number of gallons of C6H12 that need to be burned, we need to calculate the heat energy required to warm the water.
The formula to calculate heat energy is:
Q = mcΔT
Where:
Q is the heat energy in Joules (J)
m is the mass of the water in grams (g)
c is the specific heat capacity of water in J/(g of degrees Celsius)
ΔT is the change in temperature in degrees Celsius.
First, we need to convert the volume of water from cubic meters (m^3) to grams (g). We know that 1 cubic meter of water is equivalent to 1000 liters (L), and 1 liter of water is equivalent to 1000 grams.
26.4 m^3 of water = 26.4 * 1000 * 1000 g
Next, we can calculate the mass of the water:
m = 26.4 * 1000 * 1000 g
Now, we can calculate the change in temperature:
ΔT = (32.8 - 17.4) degrees Celsius
Next, we need to calculate the heat energy required:
Q = m * c * ΔT
Given that the specific heat capacity of water (c) is 4.18 J/(g of degrees Celsius), we can substitute the values into the equation:
Q = (26.4 * 1000 * 1000) * 4.18 * (32.8 - 17.4)
Finally, we need to convert the heat energy to gallons of C6H12. To do this, we need to know the energy content of C6H12, which is typically provided in units like kilojoules (kJ) or British thermal units (BTUs). Once we have that information, we can convert the heat energy to the appropriate unit and then to gallons of C6H12.