The specific heat of fat is 0.45 cal/(g) , and the density of fat is 0.94 g/cm^3 .
How much energy (in calories) is needed to heat 22 cm^3 of fat from room temperature (25 ^\circ {\rm C}) to its melting point (35 ^\circ {\rm C})?
mass fat = volume x density
q in cal = mass fat x specific heat fat (in cal/g) x (Tfinal-Tinitial)\
To calculate the energy needed to heat the fat, we can use the formula:
Q = m * c * ΔT
Where:
Q is the energy in calories
m is the mass of the fat in grams
c is the specific heat capacity of the fat in cal/(g°C)
ΔT is the change in temperature in °C
First, let's find the mass of the fat. We are given the density of fat, which is 0.94 g/cm³, and the volume of the fat, which is 22 cm³. To find the mass, we can use the formula:
mass = volume * density
mass = 22 cm³ * 0.94 g/cm³
mass = 20.68 grams (rounded to two decimal places)
Next, let's calculate the change in temperature:
ΔT = final temperature - initial temperature
ΔT = 35°C - 25°C
ΔT = 10°C
Now we have all the values needed to calculate the energy:
Q = m * c * ΔT
Q = 20.68 g * 0.45 cal/(g°C) * 10°C
Q = 93.06 calories (rounded to two decimal places)
Therefore, it would require approximately 93.06 calories of energy to heat 22 cm³ of fat from 25°C to 35°C.
To calculate the energy needed to heat the fat from room temperature to its melting point, we need to determine the mass of the fat first.
Given:
Specific heat of fat (C): 0.45 cal/(g)
Density of fat (ρ): 0.94 g/cm^3
Volume of fat (V): 22 cm^3
Change in temperature (ΔT): 35°C - 25°C = 10°C
Step 1: Calculate the mass of the fat
Since density = mass/volume, we can rearrange the equation to solve for mass:
mass = density x volume
mass = 0.94 g/cm^3 x 22 cm^3
mass = 20.68 g
Step 2: Calculate the energy using specific heat formula
The energy (Q) required to heat an object can be calculated using the specific heat formula:
Q = mass x specific heat x change in temperature
Q = 20.68 g x 0.45 cal/(g°C) x 10°C
Q = 93.06 cal
Therefore, the energy needed to heat 22 cm^3 of fat from room temperature to its melting point is 93.06 calories.