Question

Which will release more heat as it cools from ${50}^{\circ }\mathrm{C}$ to ${25}^{\circ }\mathrm{C},1\mathrm{kg}$ of water or $1\mathrm{kg}$ of aluminum? How do you know? [Section 5.5]

Short answer

1 kg of water will release more heat as it cools from 50°C to 25°C compared to 1 kg of aluminum. This is because water has a higher specific heat capacity ($4.18\times {10}^3\mathrm{J}/(\mathrm{kg}{\cdot }^{\circ }\mathrm{C})$) than aluminum (903 $\mathrm{J}/(\mathrm{kg}{\cdot }^{\circ }\mathrm{C})$), meaning it takes more energy to change the temperature of water than aluminum. The amount of heat released by water is $-1.045\times {10}^5\mathrm{J}$, while for aluminum, it is $-22,575\mathrm{J}$.

Step-by-step solution

Find the specific heat capacity values

We need the specific heat capacity of water and aluminum. For water, c = $4.18\times {10}^3\mathrm{J}/(\mathrm{kg}{\cdot }^{\circ }\mathrm{C})$ For aluminum, c = 903 $\mathrm{J}/(\mathrm{kg}{\cdot }^{\circ }\mathrm{C})$

Determine the mass and temperature change for both substances

Both substances have a mass of 1 kg and undergo a cooling process from 50°C to 25°C, resulting in a temperature change of $\Delta T=25°C-50°C=-25°C$.

Calculate the amount of heat released for each substance

Use the heat energy formula Q = mcΔT to calculate the heat energy released for water and aluminum. For water: $Q_w=m\cdot c_w\cdot \Delta T_w=(1\mathrm{kg})(4.18\times {10}^3\mathrm{J}/(\mathrm{kg}{\cdot }^{\circ }\mathrm{C}))(-{25}^{\circ }C)=-1.045\times {10}^5\mathrm{J}$ For aluminum: $Q_{Al}=m\cdot c_{Al}\cdot \Delta T_{Al}=(1\mathrm{kg})(903\mathrm{J}/(\mathrm{kg}{\cdot }^{\circ }\mathrm{C}))(-{25}^{\circ }C)=-22,575\mathrm{J}$ The negative signs indicate the substances are losing heat energy (since they are cooling down).

Compare the heat released by water and aluminum

Comparing the heat energy released by water $(-1.045\times {10}^5\mathrm{J})$ and aluminum $(-22,575\mathrm{J})$, we find that water releases more heat as it cools.

State the conclusion

As it cools from 50°C to 25°C, 1 kg of water releases more heat compared to 1 kg of aluminum. This is due to the higher specific heat capacity of water, which means it takes more energy to change its temperature compared to aluminum.