Here's the solution for Item 5: a) Help the hotel management to determine the quantity of hot water to be given to a customer for bathing. Step 1: Calculate the total mass of water required. The total volume of water for bathing is $10 \text{ litres}$. Given density of water = $1000 \text{ kgm}^{-3}$. First, convert the volume to cubic meters: $$ 10 \text{ litres} = 10 \times 10^{-3} \text{ m}^3 = 0.01 \text{ m}^3 $$ Now, calculate the total mass ($M_{\text{total}}$): $$ M_{\text{total}} = \text{Density} \times \text{Volume} = 1000 \text{ kgm}^{-3} \times 0.01 \text{ m}^3 = 10 \text{ kg} $$ Step 2: Apply the principle of calorimetry. Let $m_h$ be the mass of hot water and $m_c$ be the mass of cold water. The heat lost by the hot water must equal the heat gained by the cold water to reach the final temperature. $$ m_h c (T_h - T_f) = m_c c (T_f - T_c) $$ Where: • $T_h = 72^\circ\text{C}$ (hot water temperature) • $T_c = 20^\circ\text{C}$ (cold water temperature) • $T_f = 32^\circ\text{C}$ (final desired temperature) • $c = 4200 \text{ J kg}^{-1} \text{ K}^{-1}$ (specific heat capacity of water, which cancels out) Step 3: Set up the equation and solve for $m_h$. We know $m_c = M_{\text{total}} - m_h = 10 \text{ kg} - m_h$. $$ m_h (72^\circ\text{C} - 32^\circ\text{C}) = (10 \text{ kg} - m_h) (32^\circ\text{C} - 20^\circ\text{C}) $$ $$ m_h (40) = (10 - m_h) (12) $$ $$ 40 m_h = 120 - 12 m_h $$ $$ 40 m_h + 12 m_h = 120 $$ $$ 52 m_h = 120 $$ $$ m_h = \frac{120}{52} \text{ kg} \approx 2.3077 \text{ kg} $$ Step 4: Convert the mass of hot water to volume. $$ V_h = \frac{m_h}{\text{Density}} = \frac{2.3077 \text{ kg}}{1000 \text{ kgm}^{-3}} = 0.0023077 \text{ m}^3 $$ Convert to litres: $$ V_h = 0.0023077 \text{ m}^3 \times \frac{1000 \text{ litres}}{1 \text{ m}^3} \approx \boxed{2.31 \text{ litres}} $$ b) Advise the hotel management on how to keep the boiled water hot for a long period of time without keeping the boiler on. To keep boiled water hot for an extended period, the hotel management should focus on reducing heat loss. This can be achieved by: • Using well-insulated storage tanks (e.g., vacuum flasks or tanks with thick layers of insulating materials like foam or fiberglass) to minimize heat transfer by conduction, convection, and radiation. • Ensuring the tanks are tightly sealed with lids to prevent heat loss through evaporation and convection from the water surface. • Storing the tanks in a warm environment or away from cold drafts to reduce the temperature difference between the water and its surroundings. c) Explain to the management how the water from the boiler can reach the second floor safely. Since carrying hot water via the staircase is not allowed, the safest and most efficient method is to use a pumping system. An electric pump can be installed to draw hot water from the ground floor boiler and push it through a network of insulated pipes up to the bathrooms on the second floor. The pipes should be well-insulated to minimize heat loss during transport. Additionally, thermostatic mixing valves should be installed at the point of use in the bathrooms. These valves automatically mix the hot water from the boiler with cold water to deliver water at a safe and comfortable bathing temperature ($32^\circ\text{C}$), preventing scalding. Last free one today — make it count tomorrow, or type /upgrade for unlimited.