Assume that for a domestic hot water supply, 160 kg of water per day must be heated from to and gase — Thermodynamics and Thermochemistry Chemistry Question
Question
Assume that for a domestic hot water supply, 160 kg of water per day must be heated from $10^\circ\text{C}$ to $60^\circ\text{C}$ and gaseous fuel propane, $\text{C}_3\text{H}_8$, is used for this purpose. What volume of propane gas at STP would have to be used for heating domestic water, with efficiency of 40%? Heat of combustion of propane is –500 kcal/mol and specific heat capacity of water is 1.0 cal/K-g.
💡 Solution & Explanation
Required heat $Q = mc\Delta T = 160,000\text{ g} \times 1.0\text{ cal/g-K} \times 50\text{ K} = 8000\text{ kcal}$. At 40% efficiency, fuel heat required = $8000 / 0.40 = 20000\text{ kcal}$. Moles of propane needed = $20000 / 500 = 40\text{ moles}$. Volume at standard conditions (using $V_m \approx 22.7\text{ L/mol}$ for 1 bar pressure) = $40 \times 22.7 = 908\text{ L}$.