Let’s break down each problem step by step. --- ## **1. 10 lbs of ice from 10°F to steam at 400°F in 20 minutes – Btu/hr required** **Steps:** - Heat ice from 10°F to 32°F (sensible) - Melt ice at 32°F (latent) - Heat water from 32°F to 212°F (sensible) - Vaporize water at 212°F (latent) - Heat steam from 212°F to 400°F (sensible) **Constants:** - Specific heat of ice: **0.5 Btu/lb·°F** - Latent heat of fusion: **144 Btu/lb** - Specific heat of water: **1 Btu/lb·°F** - Latent heat of vaporization: **970 Btu/lb** - Specific heat of steam: **0.48 Btu/lb·°F** ### **Stepwise Calculation:** #### **1. Ice from 10°F to 32°F** \[ Q_1 = 10\,\text{lb} \times 0.5\,\text{Btu/lb·°F} \times (32-10)°F = 10 \times 0.5 \times 22 = 110\,\text{Btu} \] #### **2. Melt ice at 32°F** \[ Q_2 = 10\,\text{lb} \times 144\,\text{Btu/lb} = 1,440\,\text{Btu} \] #### **3. Water from 32°F to 212°F** \[ Q_3 = 10\,\text{lb} \times 1\,\text{Btu/lb·°F} \times (212-32)°F = 10 \times 1 \times 180 = 1,800\,\text{Btu} \] #### **4. Vaporize water at 212°F** \[ Q_4 = 10\,\text{lb} \times 970\,\text{Btu/lb} = 9,700\,\text{Btu} \] #### **5. Steam from 212°F to 400°F** \[ Q_5 = 10\,\text{lb} \times 0.48\,\text{Btu/lb·°F} \times (400-212)°F = 10 \times 0.48 \times 188 = 902.4\,\text{Btu} \] #### **Total Btu required:** \[ Q_{total} = Q_1 + Q_2 + Q_3 + Q_4 + Q_5 = 110 + 1,440 + 1,800 + 9,700 + 902.4 = 13,952.4\,\text{Btu} \] #### **Convert to Btu/hr (20 minutes = 1/3 hour):** \[ \text{Btu/hr} = \frac{13,952.4\,\text{Btu}}{1/3\,\text{hr}} = 13,952.4 \times 3 = \boxed{41,857\,\text{Btu/hr}} \] --- ## **2. 20 lbs of ice from 15°F to steam at 425°F in 1 hour – Btu/hr required** ### **Stepwise Calculation:** #### **1. Ice from 15°F to 32°F** \[ Q_1 = 20\,\text{lb} \times 0.5\,\text{Btu/lb·°F} \times (32-15)°F = 20 \times 0.5 \times 17 = 170\,\text{Btu} \] #### **2. Melt ice at 32°F** \[ Q_2 = 20\,\text{lb} \times 144\,\text{Btu/lb} = 2,880\,\text{Btu} \] #### **3. Water from 32°F to 212°F** \[ Q_3 = 20\,\text{lb} \times 1\,\text{Btu/lb·°F} \times (212-32)°F = 20 \times 1 \times 180 = 3,600\,\text{Btu} \] #### **4. Vaporize water at 212°F** \[ Q_4 = 20\,\text{lb} \times 970\,\text{Btu/lb} = 19,400\,\text{Btu} \] #### **5. Steam from 212°F to 425°F** \[ Q_5 = 20\,\text{lb} \times 0.48\,\text{Btu/lb·°F} \times (425-212)°F = 20 \times 0.48 \times 213 = 2,044.8\,\text{Btu} \] #### **Total Btu required:** \[ Q_{total} = Q_1 + Q_2 + Q_3 + Q_4 + Q_5 = 170 + 2,880 + 3,600 + 19,400 + 2,044.8 = 28,094.8\,\text{Btu} \] #### **Convert to Btu/hr (1 hour):** \[ \text{Btu/hr} = 28,094.8\,\text{Btu/hr} \] --- ## **3. Sensible, Latent, and Total Loads for Ventilation Air** **Given:** - **CFM:** 15 - **Outdoor:** 95°F, 40% RH, humidity ratio = 0.0088 lb/lb - **Indoor:** 68°F, 50% RH, humidity ratio = 0.0073 lb/lb ### **A. Find mass flow rate of dry air:** \[ \dot{m}_{da} = \frac{CFM \times 60}{13.33} \approx \frac{15 \times 60}{13.33} = 67.5\,\text{ft}^3/\text{hr} / 13.33 \approx 5.06\,\text{lb dry air/hr} \] Or, per minute: \[ \dot{m}_{da} = \frac{15}{13.33} = 1.125\,\text{lb dry air/min} \] But for **hourly load**, use **5.06 lb/hr**. ### **B. Sensible Load** \[ Q_{sens} = 1.08 \times CFM \times (T_{out} - T_{in}) \] \[ Q_{sens} = 1.08 \times 15 \times (95 - 68) = 1.08 \times 15 \times 27 = 1.08 \times 405 = \boxed{437.4\,\text{Btu/hr}} \] ### **C. Latent Load** \[ Q_{lat} = 4840 \times CFM \times (\text{W}_{out} - \text{W}_{in}) \] Where W is in lb/lb. \[ Q_{lat} = 4840 \times 15 \times (0.0088 - 0.0073) = 4840 \times 15 \times 0.0015 = 4840 \times 0.0225 = \boxed{108.9\,\text{Btu/hr}} \] ### **D. Total Load** \[ Q_{total} = Q_{sens} + Q_{lat} = 437.4 + 108.9 = \boxed{546.3\,\text{Btu/hr}} \] --- # **Summary Table** | Problem | Answer (Btu/hr) | Steps/Formulae Used | |---|---|---| | **1. 10 lbs ice, 10°F to 400°F steam, 20 min** | **41,857 Btu/hr** | Step-by-step phase change + sensible | | **2. 20 lbs ice, 15°F to 425°F steam, 1 hr** | **28,095 Btu/hr** | Step-by-step phase change + sensible | | **3. Ventilation loads** | Sensible: **437.4 Btu/hr**<br>Latent: **108.9 Btu/hr**<br>Total: **546.3 Btu/hr** | Load formulas | **If you need the detailed step-by-step for each calculation, let me know!**