A 10 lb. frozen boneless roast needs to be thawed and baked to a temperature of 200 degrees F.
The storage freezer maintains a temperature of -10 degrees F.
Pork changes from solid to a thawed state at 30 degrees F and has the following properties:
Heat Capacity "c" (frozen) = 0.50 BTU/(lb x F degrees)
"c" thawed = 1.2 BTU/(lb. x F degrees)
Heat of fusion (hf) = 125 BTU/lb.
How many BTUs does it take to bring the roast to a tasty 200 degrees F?
q1 is heat from -10 to 30
q1 = mass x specific heat of frozen x (Tfinal-Tinitial)
q2 = heat at 30 to thaw at 30.
q2 = mass x heat fusion
q3 = heat from 30 to 200
q3 = mass x specific heat of thawed x (Tfinal-Tinitial)
Total heat = q1 + q2 + q3
To find out how many BTUs it takes to bring the roast to 200 degrees F, we need to consider the following steps:
1. Thawing the frozen roast: The roast needs to be thawed first from -10 degrees F to its thawing temperature of 30 degrees F. To calculate the heat required for thawing, we need to find the heat of fusion, which is the amount of heat needed to convert a solid to a liquid. In this case, it is given as 125 BTU/lb.
Heat required to thaw the roast = (Mass of the roast in pounds) x (Heat of fusion)
Since we know the mass of the roast is 10 lb, the heat required for thawing is:
Heat required to thaw the roast = 10 lb x 125 BTU/lb = 1250 BTU
2. Heating the thawed roast from 30 degrees F to 200 degrees F: Once the roast is thawed, we need to heat it from 30 degrees F to the desired temperature of 200 degrees F. To calculate the heat required to do this, we need to consider the change in temperature and the specific heat capacity of the roast.
The change in temperature is given by:
Change in temperature = (Final temperature) - (Initial temperature)
Change in temperature = 200 degrees F - 30 degrees F = 170 degrees F
The specific heat capacity of the roast varies with its state. When frozen, the specific heat capacity of the roast is given as 0.50 BTU/(lb x F degrees), and when thawed, it is given as 1.2 BTU/(lb x F degrees).
To calculate the heat required to heat the roast, we can use the equation:
Heat required = (Mass of the roast in pounds) x (Specific heat capacity) x (Change in temperature)
Since the roast is thawed at this point, we will use the value of the specific heat capacity when thawed, which is 1.2 BTU/(lb x F degrees).
Heat required to heat the roast = 10 lb x 1.2 BTU/(lb x F degrees) x 170 degrees F = 2040 BTU
3. Total heat required: To find the total heat required, we can sum up the heat required for thawing and the heat required for heating the roast.
Total heat required = Heat required to thaw the roast + Heat required to heat the roast
Total heat required = 1250 BTU + 2040 BTU = 3290 BTU
Therefore, it takes 3290 BTUs to bring the 10 lb roast to a temperature of 200 degrees F.