Question

In solar-heated buildings, energy is often stored as sensible heat in rocks, concrete, or water during the day for use at night. To minimize the storage space, it is desirable to use a material that can store a large amount of heat while experiencing a small temperature change. A large amount of heat can be stored essentially at constant temperature during a phase change process, and thus materials that change phase at about room temperature such as glaubers salt (sodium sulfate decahydrate), which has a melting point of \(32^{\circ} \mathrm{C}\) and a heat of fusion of \(329 \mathrm{kJ} / \mathrm{L},\) are very suitable for this purpose. Determine how much heat can be stored in a \(5-\mathrm{m}^{3}\) storage space using (a) glaubers salt undergoing a phase change, (b) granite rocks with a heat capacity of \(2.32 \mathrm{kJ} / \mathrm{kg} \cdot^{\circ} \mathrm{C}\) and a temperature change of \(20^{\circ} \mathrm{C},\) and \((c)\) water with a heat capacity of \(4.00 \mathrm{kJ} / \mathrm{k} \cdot^{\circ} \mathrm{C}\) and a temperature change of \(20^{\circ} \mathrm{C}\).

Short answer

Question: Determine the total heat stored in a 5 m³ storage space for solar-heated buildings using three different materials: glaubers salt, granite rocks, and water. Consider the given heat capacities, temperature changes, and phase change for glaubers salt. Answer: 1. For Glaubers Salt, calculate the heat stored using heat of fusion: Heat = 329 kJ/L × 5000 L 2. For Granite Rocks, calculate the heat stored using heat capacity and temperature change: Mass = 2700 kg/m³ × 5 m³ Heat = Mass × Heat Capacity × Temperature Change 3. For Water, calculate the heat stored using heat capacity and temperature change: Mass = 1000 kg/m³ × 5 m³ Heat = Mass × Heat Capacity × Temperature Change

Step-by-step solution

Calculate Heat using Heat of Fusion

As Glaubers Salt experiences a phase change at a constant temperature, we can find the total heat stored using the heat of fusion, which is given as 329 kJ/L. We are given a storage space of 5 m³ or 5000 L. The total heat stored can be calculated using: Heat = (Heat of fusion) × (Volume) Heat = 329 kJ/L × 5000 L For Granite Rocks:

Calculate Heat using Heat Capacity and Temperature Change

For granite rocks, we are given the heat capacity (2.32 kJ/kg°C) and the temperature change (20°C). To calculate the total heat stored, we first need to find the mass of granite rocks that can be stored in 5 m³ of space. Assuming the density of granite is approximately 2700 kg/m³, we can calculate the mass stored: Mass = (Density) × (Volume) Mass = 2700 kg/m³ × 5 m³ Next, we can calculate the heat stored using the mass, heat capacity, and temperature change: Heat = (Mass) × (Heat Capacity) × (Temperature Change) For Water:

Calculate Heat using Heat Capacity and Temperature Change

For water, we are given the heat capacity (4.00 kJ/kg°C) and the temperature change (20°C). To calculate the total heat stored, we first need to find the mass of water that can be stored in 5 m³ of space. Assuming the density of water is approximately 1000 kg/m³, we can calculate the mass stored: Mass = (Density) × (Volume) Mass = 1000 kg/m³ × 5 m³ Next, we can calculate the heat stored using the mass, heat capacity, and temperature change: Heat = (Mass) × (Heat Capacity) × (Temperature Change)