When a sample of food is burned, it caused the temperature of the water in a calorimeter containing 990 g of water to increase by 8.9 celsius. Calculate the amount of heat gained by the water.

Question

When a sample of food is burned, it caused the temperature of the water in a calorimeter containing 990 g of water to increase by 8.9 celsius. Calculate the amount of heat gained by the water. What is the mass of the sample if it was 100% carbohydrates? (Carbs=4.0kcal/g)

4.18J/g c

Answer 1

In a calorimeter, the heat lost by the food (approximately) equals the heat gained by the water or:

Q_food = Q_water

We can use the equation Q = mCΔT to find the heat gained by the water since we know the water's temp increased 8.9°C (ΔT = 8.9). We can look up the Specific Heat for water and find C_water = 4.186 joules/gram/°C

Q_water = m_waterC_waterΔT_water

Q_water = (990)(4.186)(8.9) = 36883 joules or rounding to 2 sig figs, 37,000 joules

The heat given off by the food also would be 36883 joules but we are given that the energy content of the food is 4.0 kcal/g (Carbs = 4.0 kcal/g) - Notice this doesn't contain the units of temperature meaning that it already includes temp so we just need to convert our energy (36883 joules) into kcal.

Looking up the conversion of joules to kcal we see that 1 kcal = 4184 j so 36883 j = 8.8 kcal

Q_food = m_food•(energy content of the food)

8.8 = m_food•(4.0)

m_food = 8.8/4.0 = 2.2 grams