Let's analyze and solve this problem step-by-step: --- ## Step 1: **Identify the components involved** - **Building dimensions:** 3 m × 4 m (area 12 m²) - **Wall area:** 10 m² (of face brick) - **Indoor temperature:** 25°C - **Outdoor temperature:** 32°C - **Maximum indoor temperature:** 22°C - **Window area:** 2 m² - **U-value of window:** 6 W/m²·K - **Glass area:** 2 m² - **SHGF (solar heat gain):** 350 W/m² - **People:** 2 persons, each with 150 W heat generation, with a sensible heat factor of 55% - **Lighting:** 20 W/m² - **Office equipment:** 15 W/m² with 50% sensible heat factor - **Cooling load factors:** - Shading coefficient (SC): .65 - Cooling load factor (CLF): .83 --- ## Step 2: **Calculate heat gain from the wall** The heat transfer through the wall: \[ Q_{wall} = U_{wall} \times A_{wall} \times \Delta T \] But since the U-value of the face brick wall isn't given, and the problem focuses on other heat gains, we can proceed to sum other heat gains directly, assuming the wall's contribution is included in overall heat transfer calculations or negligible for this context. --- ## Step 3: **Calculate heat gain from the window** The heat transfer through the window: \[ Q_{window} = U_{window} \times A_{window} \times (T_{outdoor} - T_{indoor}) \] \[ Q_{window} = 6\, \text{W/m}^2\cdot \text{K} \times 2\, \text{m}^2 \times (32°C - 25°C) = 6 \times 2 \times 7 = 84\, \text{W} \] --- ## Step 4: **Calculate solar heat gain through the window** \[ Q_{solar} = \text{SHGF} \times \text{area} \times \text{shading coefficient} \] \[ Q_{solar} = 350\, \text{W/m}^2 \times 2\, \text{m}^2 \times .65 = 350 \times 2 \times .65 = 455\, \text{W} \] --- ## Step 5: **Calculate heat gain from people** Each person generates 150 W, with 55% being sensible: \[ Q_{people} = 2 \times 150\, \text{W} \times .55 = 2 \times 82.5 = 165\, \text{W} \] --- ## Step 6: **Calculate heat gain from lighting** \[ Q_{lights} = 20\, \text{W/m}^2 \times \text{area} = 20 \times 12 = 240\, \text{W} \] --- ## Step 7: **Calculate heat gain from office equipment** \[ Q_{equipment} = 15\, \text{W/m}^2 \times 12\, \text{m}^2 = 15 \times 12 = 180\, \text{W} \] Considering only the sensible heat component (50% of total): \[ Q_{equipment,sensible} = 180 \times .5 = 90\, \text{W} \] --- ## Step 8: **Sum all internal heat gains** \[ Q_{internal} = Q_{people} + Q_{lights} + Q_{equipment,sensible} \] \[ Q_{internal} = 165 + 240 + 90 = 495\, \text{W} \] --- ## Step 9: **Calculate total heat gain** Total heat gain includes: - Heat transfer through the window: 84 W - Solar heat gain: 455 W - Internal heat gains: 495 W \[ Q_{total} = 84 + 455 + 495 = 1034\, \text{W} \] --- ## Step 10: **Apply shading coefficient and cooling load factor** Adjusted heat gain considering shading and cooling load: \[ Q_{adjusted} = Q_{total} \times SC \times CLF \] \[ Q_{adjusted} = 1034 \times .65 \times .83 \] \[ Q_{adjusted} \approx 1034 \times .5395 \approx 557.4\, \text{W} \] --- ## **Final Answer:** The **total cooling load** for the office is approximately **557.4 W**. --- If you need further clarification or detailed calculations for specific parts, feel free to ask!