In lab, Will burns a 0.6-g peanut beneath 50 g of water, which increases in temperature from 22°C to 50°C. The amount of heat absorbed by the water can be found with the equation ?Q? = cm? ? ?T,? where ?Q? is the amount of heat, ?c? the specific heat of water, ?m? the mass of water, and ? ?T? the change in the water’s temperature. a. Assuming that 40% of the heat released makes its way to the water, show that the food value of the peanut is 3500 calories, or 3.5 Calories. b. What is the food value in calories per gram? In Calories per gram?

Solution 1P Step 1: Peanut mass is 0.6 grams. The mass of water is 50 grams. The temperature increase is, T = T T = 50 C 22 C = 28 C 0 2 1 The specific heat of water is, 1 Cal/gram C . The heat absorbed by the water is, Q = C × mass × temperature increase [where C is the specific heat] = 1 × 50 × T = 1 × 50 × 28 = 1400 Cal.