Heat Capacity and Calorimetry Question 3

A $\pu{1.0 g}$ sample of a cashew was burned in a calorimeter containing $\pu{1000}$ . $\pu{g}$ of water, and the temperature of the water changed from $20.0^\circ \pu{C}$ to $25.0^\circ \pu{C}$ . In another experiment, a 3.0 g sample of a marshmellow was burned in a calorimeter containing $2000$ . $\pu{g}$ of water, and the temperature of the water changed from $25.0^\circ \pu{C}$ to $30.0^\circ \pu{C}$ . Based on the data, which of the following can be concluded about the energy content for $\pu{1.0 g}$ of each of the two substances? (The specific heat of water is $\pu{4.2 J}/(\pu{g\cdot ^\circ}\pu{C})$ .)

The combustion of

\pu{1.0 g}

of cashew releases less energy than the combustion of

\pu{1.0 g}

of marshmellow.

The combustion of

\pu{1.0 g}

of cashew releases the same amount of energy as the combustion of

\pu{1.0 g}

of marshmellow.

The combustion of

\pu{1.0 g}

of cashew releases more energy than the combustion of

\pu{1.0 g}

of marshmellow.

No comparison can be made because the two systems started with different masses of food, different masses of water, and different initial temperatures.

Approach

We can calculate the amount of heat energy transferred by each food item:

q_{\text{cashew}}= q_{\text{water}} = mc\Delta T

= (1000)(4.2)(25-20)

\approx \pu{20,000 J}

q_{\text{marshmellow}}= q_{\text{water}} = mc\Delta T

= (2000)(4.2)(30-25)

\approx \pu{40,000 J}

Note that the $\pu{20,000 J}$ was transferred from $\pu{1.0}$ grams of cashew, whereas the $\pu{40,000 J}$ was transferred from $\pu{3.0}$ grams of marshmellow.

The marshmellow transfers $\dfrac{40{,}000}{3} \pu{J}$ of energy per gram, which is significantly less than $\pu{20,000 J}$ .