In lab, Will burns a 0.6 g peanut beneath 48 g of water, which increases in temperature from 22 degree C to 55 degree C. The amount of heat absorbed by the water can be found with the equation Q =cm \Delta T, where Q is the amount of heat, c the specific heat of water, m the mass of water, and \Delta T the change in the water's temperature.
Assuming that 38 % of the heat released makes its way to the water, find the food value of the peanut.
heat into water = .38*heat out of peanut
48* Cw in cal/gm deg c * (55-22)/.38 = heat out of peanut in calories
divide by 1000 to get kilocalories(food calories)
that is the calories out of the peanut per 0.6 gram of peanut
if you want the kilocalories per gram divide by 0.6
To find the food value of the peanut, we first need to calculate the amount of heat released by the peanut. Since 38% of this heat is absorbed by the water, we can use the equation Q = cmΔT to calculate the amount of heat absorbed by the water.
Given:
Mass of water (m) = 48 g
Change in temperature (ΔT) = 55°C - 22°C = 33°C
Specific heat of water (c) = 4.186 J/g°C (at constant pressure)
Step 1: Calculate the amount of heat absorbed by the water.
Q = cmΔT
Q = (48 g)(4.186 J/g°C)(33°C)
Q ≈ 66872.064 J (rounded to four decimal places)
Step 2: Calculate the total amount of heat released by the peanut.
Since 38% of the heat released makes its way to the water, we can find the total heat released by dividing the heat absorbed by the water by 0.38.
Total heat released = (Q absorbed by water) / 0.38
Total heat released = 66872.064 J / 0.38
Total heat released ≈ 175975.962 J (rounded to four decimal places)
Step 3: Convert the heat released to food value.
The food value of the peanut can be approximated as the total heat released in calories, since 1 calorie is approximately equal to 4.184 J.
Food value = Total heat released / 4.184
Food value ≈ 42075.050 calories (rounded to three decimal places)
Therefore, the food value of the peanut is approximately 42075.050 calories.
To find the food value of the peanut, we need to calculate the amount of heat absorbed by the water.
First, let's calculate the amount of heat absorbed by the water using the equation Q = cmΔT:
Q = (c * m * ΔT)
Given:
- c (specific heat of water) is approximately 4.18 J/g°C
- m (mass of water) is 48 g
- ΔT (change in the water's temperature) is (55°C - 22°C) = 33°C
Now substitute the given values into the equation:
Q = (4.18 J/g°C) * (48 g) * (33°C)
Q = 6,542.56 J
Next, we need to find the total heat released by the peanut. We are told that 38% of the heat released by the peanut makes its way to the water.
Let F be the food value of the peanut.
Total heat released by the peanut = Food value (F) + Heat absorbed by water
Since 38% of the heat released by the peanut goes to the water, we can write:
0.38 * Total heat released by the peanut = Heat absorbed by water
0.38 * F = 6,542.56 J
To find the food value (F) of the peanut, we need to solve for F:
F = 6,542.56 J / 0.38
F ≈ 17,219.89 J
The food value of the peanut is approximately 17,219.89 J.