Problem 3. Let's say we have a big bathroom, which measures 12' x 12' with 10' tall ceilings,and in this room there are 18 light bulbs. If we use 60

W incandescent light bulbs, how much warmer would this bathroom be after 1 hour compared to if we were using our beloved 8.5 W LED bulbs. Assume that 50% of the heat from the light bulbs is transferred to the air (the rest of the heat is transferred to the walls or escapes otherwise). Incandescent bulbs convert ~5% of their input energy (60 W) to light and the rest to heat, the LED bulbs convert ~25% of input energy (8.5 W) to light and the rest to heat. The specific heat capacity of air is 0.24 Btu/(lb*°F)and the mean molecular weight of air is 29 g/mol. Assume that the bathroom's air temperature starts at 76 °F (298 K) and 1 atm of pressure. Conversions: 1 kg =2.2 lb; 28.32 L= 1 ft³; 1 kW*hr = 3412 BTU. Use the ideal gas law PV=nRT to calculate the mass of air in the room (assume mass calculated at 76 F is constant even with warming (and ignore PV changes).