Cooling a Radio Transmitter Room
A radio room at a training facility contains equipment that dissipates a constant 1,500 W of heat. The room measures 5 m × 4 m × 3 m. An air conditioner rated at 2,000 W of cooling is installed. During a test, the room temperature stabilizes at 32 °C while the outside air is 24 °C, and the walls have a thermal resistance such that heat leaks in at 8 W per °C of temperature difference between inside and outside. A technician concludes the air conditioner is faulty because the room is still warm. The equipment must stay below 28 °C to operate reliably.
1. Using an energy balance, determine the actual heat load on the air conditioner and judge whether it is faulty.
Read the worked answer
Heat sources:
- Equipment: 1,500 W (constant).
- Wall leakage: 8 W/°C × (32 − 24) = 8 × 8 = 64 W.
Total load: 1,500 + 64 = 1,564 W.
Comparison: The unit is rated at 2,000 W cooling, which exceeds 1,564 W. The unit is not faulty - it is removing more heat than is being generated.
Why the room is warm anyway: The set point or thermostat may be set too high, or the unit is simply holding equilibrium at 32 °C rather than driving to 28 °C. The technician's conclusion is premature; the balance shows capacity exists.
2. Determine the maximum inside temperature the system can be driven to, and state whether the 28 °C requirement can be met.
Read the worked answer
At equilibrium, cooling = load:
2,000 = 1,500 + 8(T_in − 24)
500 = 8(T_in − 24)
T_in − 24 = 62.5 → T_in = 86.5 °C.
This is the theoretical equilibrium if the unit ran at full rated capacity; it shows the unit has ample capacity. In practice the thermostat controls the set point, so the room can be held below 28 °C provided the thermostat is set correctly and airflow is adequate. The 28 °C requirement is achievable; the observed 32 °C reflects a control setting, not a capacity shortfall.