3. In an air heating system, the outside air at t_(1)=-15^circ C is heated in a duct heater at p=const to 60^circ C How much heat must be expended to heat 1000m^3 of air? Consider the heat ca- pacity of the air as constant. Take the air pressure as 760 mm Hg.

Question

3. In an air heating system, the outside air at t_(1)=-15^circ C is heated in a duct heater at p=const to 60^circ C How much heat must be expended to heat 1000m^3 of air? Consider the heat ca- pacity of the air as constant. Take the air pressure as 760 mm Hg.

Answer 1

To solve this problem, we need to use the formula for the heat required to change the temperature of a gas:Q = m * Cp * ΔTWhere:- Q is the heat required (in Joules)- m is the mass of the air (in kg)- Cp is the specific heat capacity of air (in J/kg·K)- ΔT is the change in temperature (in K)Given information:- Initial temperature, t1 = -15°C = 258.15 K- Final temperature, t2 = 60°C = 333.15 K- Volume of air, V = 1000 m³- Air pressure, p = constant (not given the value, but we can assume it to be 1 atm or 101.325 kPa)Step 1: Calculate the mass of the air.Density of air, ρ = p / (R * T)Where:- R is the specific gas constant for air, R = 0.287 kJ/kg·K- T is the absolute temperature in Kρ = 101.325 kPa / (0.287 kJ/kg·K * 333.15 K) = 1.186 kg/m³Mass of air, m = ρ * V = 1.186 kg/m³ * 1000 m³ = 1186 kgStep 2: Calculate the change in temperature.ΔT = t2 - t1 = 333.15 K - 258.15 K = 75 KStep 3: Calculate the specific heat capacity of air.Cp = 1.005 kJ/kg·KStep 4: Calculate the heat required.Q = m * Cp * ΔTQ = 1186 kg * 1.005 kJ/kg·K * 75 KQ = 89,427.5 kJTherefore, the heat required to heat 1000 m³ of air from -15°C to 60°C is 89,427.5 kJ.

Вопрос

3. In an air heating system, the outside air at t_(1)=-15^circ C is heated in a duct heater at p=const to 60^circ C How much heat must be expended to heat 1000m^3 of air? Consider the heat ca- pacity of the air as constant. Take the air pressure as 760 mm Hg.

Решения

Ответ