COULD YOU FURTHER EXPLAIN HOW MANY BTU ARE REQUIRED TO RAISE THE TEMP OF500 GALLONS OF WATER FROM 70 DEGRESS TO 160 DEGREES FAHRENHIET
As Bob Pursley said
In general:
heat=mass*specificeheat*changetemp
or
heat in = mass of water * specific heat of water * (Final temp -original temp)
In these strange English units
weight in pounds is used for mass
weight = 500 gal * 8.31 pounds/gal = 4155 pounds
specific heat of water in these units = 1 BTU/pound
change in temp = 160 - 70 = 90 degrees F
so
BTU = 4155 * 1 * 90
= 373,950 BTU
There is no change of state in this problem. If you were changing water to vapor that would require an extra 970 btu/lb or 4,030,350 on top of the 373,950 grid.
Certainly! To calculate the number of BTUs (British Thermal Units) required to raise the temperature of a substance, we need to use the following formula:
Q = mcΔT
Where:
Q is the energy required (in BTUs)
m is the mass of the substance (in pounds)
c is the specific heat capacity of the substance (in BTU/lb·°F)
ΔT is the temperature change (in °F)
In your case, we need to convert the volume of water from gallons to pounds, as well as consider the specific heat capacity of water.
1. Converting gallons to pounds:
Since the density of water is approximately 8.34 pounds per gallon, we can calculate the mass of 500 gallons of water:
Mass = Volume × Density
Mass = 500 gallons × 8.34 pounds/gallon
2. Calculating the temperature change:
We need to find the temperature difference, ΔT, between the starting temperature (70°F) and the desired temperature (160°F):
ΔT = Final Temperature - Initial Temperature
3. Determining the specific heat capacity of water:
The specific heat capacity of water is approximately 1 BTU/lb·°F. This means it takes 1 BTU to raise the temperature of 1 pound of water by 1°F.
Now, we can plug in the values into the formula to find the energy required (Q):
Q = m × c × ΔT
Note: Ensure that all units are consistent (pounds, BTU, and °F). Let's carry out the calculations.
Mass = 500 gallons × 8.34 pounds/gallon
ΔT = 160°F - 70°F
c = 1
Now, substitute these values into the formula:
Q = (500 gallons × 8.34 pounds/gallon) × 1 BTU/lb·°F × (160°F - 70°F)
Calculating this will give you the number of BTUs required to raise the temperature of 500 gallons of water from 70°F to 160°F.