A 2.5 g sample of a pretzel is burned completely. The heat it gives off is used to heat 45 g of water from 22 °C to 51 °C. What is the energy value of the pretzel in kcal/g

Answer 1

Hello, Gary,

We need to know the specific heat of the water that absorbed the energy. This is a physical constant that is different for each material, and can be written with different units (e.g., Joules or calories, grams or moles, temperature of C, F, or K, and so on. Since you need the answer expressed in kcal/g, I looked up a convenient specific heat of water having those units. Water has a specific heat of 1.00 kcal/kg*K, In other words, it takes 1,000 calories (1 kcal) to raise the temperature of 1 kg of water by 1 degree K. We can also express this as 1.00 kcal/kg*C, since the changes in both C and K are the same.

The thermodynamic equation that ties these together is:

q = cm(T1 - T2),

where q is the heat, c is the specific heat, m is the mass (or moles) and (T1 - T2) is the temperature change. We want to calculation the heat released, or q, in kilocalories. Note that the value for c is in kg, so we must first convert the 45g into kilograms by dividing it by 1000(g/kg). Since we are subtracting the final temperature from the first, the difference will be the same for both C and K units, so T1-T2 = -29K

q = 1.0kcal/(kg*K) * 0.045kg*(-29K)

q = -1.3 kcal for the total energy released (it is negative since this is the energy leaving the pretzel. To get the energy per gram, we divide by 2.5g. I get -0.52 kcal/g. [NOTE: This was corrected as per the comment by J.R. S., below.]

I hope this helps,

Bob