Please show each step: Tony burns a 0.6 gram peanut submerged in 50 grams of water, which increases its temperature from 22 to 50 ° C. a) Assuming an efficiency of 40%, calculate the nutritional value of the peanut. b) Demonstrate that the nutritional value in calories per gram.
nutritional value=heat/mass
heat=masswater*specificheatwater*changintemp
so divide the heat in the water by .4, and you have the heat of the nut. Solve for nutritional value.
To calculate the nutritional value of the peanut, we need to determine the amount of energy transferred to the water by burning the peanut and then convert it into calories per gram.
a) The first step is to calculate the heat transfer by using the formula:
Q = m * c * ΔT
where Q is the heat transfer, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
In this case, we need to consider the water. The mass of water is 50 grams, specific heat capacity of water (c) is 4.18 J/g°C, and the change in temperature (ΔT) is 50°C - 22°C = 28°C.
Q = 50 g * 4.18 J/g°C * 28°C
Q = 5852 J (Joules)
b) Now that we have the heat transfer value in joules, we can convert it into calories.
The conversion factor is 1 calorie (cal) = 4.18 joules (J).
So, the nutritional value of the peanut is:
Nutritional Value = 5852 J * 0.40 (efficiency) / 4.18 J/cal
Nutritional Value = 558.37 cal
Now, to determine the nutritional value in calories per gram, we divide the nutritional value by the mass of the peanut:
Nutritional Value per gram = 558.37 cal / 0.6 g
Nutritional Value per gram = 930.62 cal/g
Therefore, the nutritional value of the peanut is approximately 930.62 calories per gram.