Answer:
The exit temperature of the gas = 32° C
Explanation:
Solution
Given that:
Inlet temperature T₁ = 27°C ≈ 300.15 K
Inlet pressure P₁ = 100 KPa = 100 * 10^3 Pa
Volume flow rate , V = 15 m/s³
Diameter of the deduct, D = 500 mm = 0.5 m
Electric heater power, W heater = 130 kW = 130 * 10^3 W
The heat lost Q = 80 kW = 80 * 10^3 W
Now,
From the ideal gas law, density of the air at the inlet is given as :
ρ₁ = P₁/RT₁ = 100 * 10^3/500 * 300
=0.6667 kg/m³
The mass flow rate through the duct is computed below:
m = ρ₁ V = 0.6667 * 15 = 10 kg/s
Thus
Applying the first law of thermodynamics to the process is shown below:
Q + m (h₁ + V₁²/2 + gz₁) = m (h₂ + V₂²/2 + gz₂) + W (Conservation energy)
So,
If we neglect the potential and kinetic energy changes of the air, the above equation can be written again as:
Q + m (h₁) = m (h₂) + W
or
Q - W heater =m (h₂ - h₁) or Q - W heater =m (T₂ - T₁)
Thus
h₂ - h₁ = Cp T₂ - T₁
Now by method of substitution the known values are:
(- 80 *10^3) - (-130 * 10^3) = 10 * 100 * (T₂ -27)
Note: The heat transfer is taken as negative because the heat is lost by the gas and work done is also taken as negative because the work is done on the gas
So,
Solving for T₂,
T₂ = 32° C
Therefore the exit temperature of the gas = 32° C
