Building physics First call – 13/01/23 – exercises
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Building physics
First call – 13/01/23 – exercises
FIRST PART
Exercise 1 (2 pts)
A heat engine with an efficiency of 40% receives 1 kW of heat from a source at 1000 K and discharge heat to a sink at 300 K. Calculate the change of the entropy of the universe per unit of time due to the operation of the heat engine.
Exercise 2 (2 pts)
1 mol of helium (monoatomic ideal gas with molar mass of 4 g/mol) initially at a temperature of 900 K and a pressure of 10 bar expands adiabatically to a pressure of 2 bar. Calculate the temperature at the end of the expansion and the exchanged work.
Exercise 3 (2 pts)
A heat exchanger is used to evaporate saturated water at 5 bars using a stream of 10 kg/s of diathermic oil (specific heat of 1.52 kJ/(kg K)), which enters the heat exchanger at 220 °C and leaves at 150 °C. Calculate the mass flow rate of evaporated water.
Exercise 4 (2 pts)
A compressor is used to compress Nitrogen (diatomic ideal gas with molar mass of 28 g/mol) from 1 bar and 5 °C to 200 bars. Calculate the outlet temperature and the power needed to run the compressor if its isentropic efficiency is 75% and the Nitrogen flowrate is equal to 0.5 kg/s.
Exercise 5 (2 pts)
During winter a volumetric flowrate of external air of 1000 m3/h at 0 °C and 70% of relative humidity is heated up at a temperature of 30 °C. Successively, the air is mixed with a mass slow rate of 500 kg/h of indoor air at 20 °C and 50% of relative humidity. Calculate the properties (temperature, enthalpy, and absolute humidity) of the mixed air.
Exercise 6 (2 pts)
Calculate the U-value and the heat transfer rate through a wall which stratigraphy is reported in the table below, when the operating temperature and convective-radiative heat transfer coefficient are 35 °C and 20 W/(m2 K) for the outdoor environment and 26 °C and 8 W/(m2 K) for the indoor environment.
|
Material |
Thickness cm |
Conductivity W/(m K) |
Resistance m2 K/W |
|
Plaster |
1 |
0.80 |
|
|
Brick |
15 |
0.36 |
|
|
Cavity |
5 |
|
0.22 |
|
Brick |
15 |
0.36 |
|
|
Plaster |
1 |
0.80 |
|
Exercise 7 (2 pts)
During a winter night the floor of a terrace exchange heat by convection with the air (Tair = 0 °C) and by radiation with the sky (Tsky = -20 °C) with a view factor of 1. Assuming an emissivity of 0.9, a convective heat transfer coefficient of 15 W/(m2 K), calculate the temperature of the floor under steady state conditions.
Exercise 8 (2 pts)
Water flows inside a pipe with an average temperature of 62 °C and velocity of 1 m/s in conditions of forced convection. Considering that the internal diameter is equal to 200 mm, please determine the internal heat transfer coefficient by choosing the correct correlation.
Choose the correct correlation for the calculation of the internal heat transfer coefficient:
. Laminar flow: Nu = 3.66 (Re < 2300)
. Turbulent flow: Nu = 0.023 ∙ Re0.8 ∙ Pr3/1 (Re > 10.000)
The properties of water at a temperature of 62 °C (335.15 K) are provided in the table below.
|
Thermophysical properties of water at 335 K |
||
|
p |
982 |
kg/m3 |
|
|
4.186 |
kJ/(kg K) |
|
v |
4.6 ∙ 10-7 |
m2/s |
|
λ |
0.656 |
w/(m K) |
SECOND PART
Exercise (8 pts)
Consider a simplified apartment with the following characteristics:
- Surfaces: floor of 100 m2 towards another heated apartment, walls of 140 m2 (including the window surface), window of 20 m2, roof towards the external environment.
- U-values: walls 0.2 W/(m2 K); window 1.1 W/(m2 K).
- Thermal bridge coefficient between window and wall: 0.05 W/(m K), with a overall thermal bridge length of 25 m.
- Air exchange rate due to infiltration: 0.4 h- 1.
- Internal air volume: 300 m3.
Calculate, assuming an indoor temperature of 20 °C, an outdoor temperature of -5 °C, an internal heat transfer coefficient of 8 W/(m2 K) and an external heat transfer coefficient of 25 W/(m2 K):
[1] The heat load due to infiltration.
[2] The heat transfer through the walls (including windows and thermal bridges).
[3] The overall heating load.
The building is heated by a heat pump with a COP which is 40% of the COP of an ideal heat pump operating between the same temperatures, which are the air temperature and the supply temperature to the heating system (40 °C). Calculate:
[4] The power required to run the heat pump.
2024-01-03