A 0.6-g peanut is burned beneath 50 g of water, which increases in temperature from 22degreesC to 50 degreesc. What is the exact food value of the peanut? (Assuming a 40% efficiency)
Oh, peanuts! They're not just delicious snacks, they're also energy powerhouses! Now, let me calculate the exact food value of this tiny but mighty peanut for you.
First things first, let's find out how much energy is required to heat up the water. We can use the formula Q = mcΔT, where Q is the energy absorbed, m is the mass of water, c is the specific heat capacity of water (which is 4.18 J/g°C), and ΔT is the change in temperature.
So, for 50 grams of water, the energy absorbed is:
Q = (50 g) * (4.18 J/g°C) * (50°C - 22°C)
Q = 50 g * 4.18 J/g°C * 28°C
Q ≈ 5860 J
Now, remember that the efficiency is given as 40%. Efficiency measures how much of the energy released by the peanut is actually used. So, to find the food value, we need to divide the energy absorbed by the efficiency:
Food Value = (Energy Absorbed) / (Efficiency)
Food Value ≈ 5860 J / 0.40
Food Value ≈ 14650 J
Therefore, the exact food value of this peanut is approximately 14650 joules. That's one mighty peanut!
To calculate the food value of the peanut, we can use the concept of heat transfer.
Step 1: Calculate the heat absorbed by the water
The specific heat capacity of water is 4.18 J/g°C. The mass of water is 50 g, and the temperature change is ΔT = 50°C - 22°C = 28°C. Therefore, the heat absorbed by the water can be calculated using the formula:
Qwater = mwater × Cwater × ΔT
= 50 g × 4.18 J/g°C × 28°C
Step 2: Calculate the heat released by the peanut
The heat released by the peanut is equal to the heat absorbed by the water. However, since the system is not 100% efficient, we need to adjust for the efficiency. The heat released by the peanut can be calculated using the formula:
Qpeanut = Qwater / Efficiency
= Qwater / 0.40
Step 3: Calculate the food value of the peanut
The food value of the peanut is the energy content, which can be calculated using the formula:
Food Value = Qpeanut / mass of the peanut
= Qpeanut / 0.6 g
Now, let's calculate the exact food value of the peanut.
Qwater = 50 g × 4.18 J/g°C × 28°C
= 58,760 J
Qpeanut = Qwater / Efficiency
= 58,760 J / 0.40
= 146,900 J
Food Value = 146,900 J / 0.6 g
= 244,833.33 J/g
Therefore, the exact food value of the peanut is approximately 244,833 J/g.
To calculate the exact food value of the peanut, we can use the concept of energy transfer. The energy released by burning the peanut heats up the water. We can use the equation:
Q = m * C * ΔT
Where:
Q is the amount of heat transferred,
m is the mass of the substance (water in this case),
C is the specific heat capacity of the substance, and
ΔT is the change in temperature.
In this case, we need to find the heat (Q) released by burning the peanut.
Step 1: Calculate the heat absorbed by the water
Using the equation above, we can calculate the heat absorbed by the water:
Q_water = m_water * C_water * ΔT_water
m_water = 50 g (mass of water)
C_water = 4.184 J/g°C (specific heat capacity of water)
ΔT_water = 50°C - 22°C (change in temperature of water)
Step 2: Calculate the heat released by the peanut
Since the peanut is burned, the heat released is equal to the amount of heat absorbed by the water.
Q_peanut = Q_water
Step 3: Calculate the energy value of the peanut
The food value of the peanut is equivalent to the energy released by burning it. However, we need to consider the efficiency of the process.
Efficiency = (Q_peanut / Food Value) * 100%
Rearranging the equation:
Food Value = Q_peanut / (Efficiency / 100%)
Step 4: Substitute the values and calculate the exact food value of the peanut
Substitute the values into the equation and solve for the food value:
Food Value = Q_peanut / (40 / 100)
Finally, we can calculate the exact food value of the peanut by substituting the calculated values:
Food Value = Q_peanut / 0.4
To find the exact food value, we need the value of Q_peanut, which we calculated in step 2.
heat to water = mass x specific heat x delta T.
mass of water = 50 g in the problem.
specific heat water = 1 calorie/gram*C
delta T = 50-22 = 28 degrees.
Calculate heat produced by the peanut to heat the water. Let's call that value x.
If the process was only 40% efficient, then
x/0.40 = all of the heat produced which we will call ??. That is the food value of the peanut.
Now here you can get into an argument since what I have calculated is the number of calories for the 0.6 g peanut. My calculations give a value of about 5800 calories OR about 5.8 kilocalories. (you need to do the exact math). Why the argument? Many foods, in calorie tables, show the calorie content as kilocalories BUT (and this is an important BUT) they call it calories. When your problem says to list the EXACT FOOD VALUE of the peanut, it makes me think they want the so-called BIG calorie and that is the kilocalorie so I would list 5.8; however, about 5800 calories is the correct answer. You may have a multiple guess answer sheet and that may be of some help in knowing what answer they want.