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.
Find the change in heat content of a peanut when it's mass is 0.6g which is burnt in 25 to 90 degree Celsius in volume of 10ml of water
To calculate the nutritional value of the peanut, we need to determine the amount of energy transferred from the peanut to the water.
a) To calculate the amount of energy transferred, we can use the equation:
Energy transferred = mass of water × specific heat capacity of water × change in temperature of water
First, let's calculate the energy transferred:
Energy transferred = 50 g × 4.18 J/g°C × (50°C - 22°C)
Energy transferred = 50 g × 4.18 J/g°C × 28°C
Energy transferred = 58840 J
Since the efficiency is given as 40%, we need to calculate the actual nutritional value. The efficiency represents the fraction of energy that is transferred as useful energy. In this case, useful energy is the energy that the body can use from the peanut.
Actual nutritional value = efficiency × energy transferred
Actual nutritional value = 0.40 × 58840 J
Actual nutritional value = 23536 J
b) To determine the nutritional value in calories per gram, we need to convert the energy from joules to calories. There are 4.18 J in 1 calorie.
Nutritional value in calories = Actual nutritional value / 4.18
Nutritional value in calories = 23536 J / 4.18
Nutritional value in calories = 5630.14 calories
Finally, to determine the nutritional value per gram, we divide the nutritional value in calories by the mass of the peanut:
Nutritional value per gram = Nutritional value in calories / 0.6 g
Nutritional value per gram = 5630.14 calories / 0.6 g
Nutritional value per gram ≈ 9383.57 calories/gram
Therefore, the nutritional value of the peanut is approximately 9383.57 calories per gram.