how much heat must be removed from 14 lbs of aluminum block in order to cool it from 80 degrees fahrenheit to 15 degrees fahrenheit?

To calculate the amount of heat that needs to be removed from the aluminum block, you can use the specific heat capacity equation:

Q = m * c * ΔT

where:
Q = heat energy
m = mass (in pounds)
c = specific heat capacity (in BTU/lb·°F)
ΔT = change in temperature (in °F)

The specific heat capacity of aluminum is approximately 0.217 BTU/lb·°F.

First, let's convert the mass from pounds to grams:
14 lbs * 453.592 g/lb = 6354.688 g

Next, let's calculate the change in temperature:
ΔT = 80°F - 15°F = 65°F

Now we have all the values we need to calculate the heat energy:
Q = 6354.688 g * 0.217 BTU/lb·°F * 65°F

Converting grams to pounds:
6354.688 g * 0.00220462 lb/g = 14.001 lbs (approximately)

Calculating the heat energy:
Q = 14 lbs * 0.217 BTU/lb·°F * 65°F
Q ≈ 197.355 BTU

Therefore, approximately 197.355 BTU of heat needs to be removed from the aluminum block to cool it from 80 degrees Fahrenheit to 15 degrees Fahrenheit.

To find out how much heat needs to be removed from the aluminum block, we can use the specific heat capacity equation:

Q = mcΔT

Where:
Q is the amount of heat energy (in calories or joules)
m is the mass of the aluminum block (in pounds or kilograms)
c is the specific heat capacity of aluminum (in calories per pound per degree Fahrenheit or joules per kilogram per degree Celsius)
ΔT is the change in temperature (in degrees Fahrenheit or degrees Celsius)

First, we need to convert pounds to kilograms because the specific heat capacity of aluminum is usually given in joules per kilogram per degree Celsius.

1 pound is approximately 0.4536 kilograms.

So, the mass of the aluminum block is:
m = 14 lbs * 0.4536 kg/lb = 6.3492 kg

Next, we need to convert Fahrenheit to Celsius because the change in temperature should be in degrees Celsius.

ΔT = 80°F - 15°F = 65°F

To convert Fahrenheit to Celsius, we'll use the formula:
C = (F - 32) * 5/9

ΔT = (65°F - 32) * 5/9 = 17.2222°C

Now, we need to find the specific heat capacity of aluminum. The specific heat capacity of aluminum is approximately 0.897 J/g°C.

To convert the specific heat capacity to joules per kilogram per degree Celsius, we'll divide by 1000 because there are 1000 grams in a kilogram.

c = 0.897 J/g°C / 1000 g/kg = 0.000897 J/g°C

Now we can substitute these values into the equation:

Q = mcΔT

Q = (6.3492 kg) * (0.000897 J/g°C) * (17.2222 °C)

Calculating the equation will give us the amount of heat energy needed to be removed from the aluminum block in joules.