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Building physics

Second call – 27/01/23 – exercises

Exercise 1 (2 pts)

A heat engine receives 1000 W of energy from a source at 700 K and produces 600 W of work, while discharging heat to a low temperature sink at 300 K. Calculate the efficiency of the engine and determine whether it is acceptable based on the second law of thermodynamics.

(0.6 → not possible because higher than the Carnot efficiency)

Exercise 2 (2 pts)

A closed system contains 2 mol of helium (ideal monoatomic gas with molar mass of 4 g/mol) at 400 °C and 2 bar. Calculate the final temperature and the exchanged work when a heat of 2000 J is provided to the system along an isobaric transformation.

(721.3 K ;800 J)

Exercise 3 (2 pts)

A mass flow rate of 100 kg/s of steam enters a turbine at the temperature of 300 °C and a pressure of 2 MPa. Calculate the isentropic efficiency of the turbine and the exchanged work knowing that the outlet pressure is 10 kPa and the vapor quality at the outlet is 0.85.

(0.907; 77.91 MW)

Exercise 4 (2 pts)

A volumetric flowrate equal to 1000 m3/h at 30 °C and 60% of relative humidity is cooled down to a temperature of 15 °C. Calculate the cooling power required and the mass flow rate of condensate produced.

(9.22 kW; 1.72 g/s)

Exercise 5 (2 pts)

A wall characterized by a U-value of 0.8 W/(m2 K) separates an indoor ambient at 20 °C and with 70% as relative humidity from the outdoor environment at - 10 °C. Determine whether there is surface condensation on the internal wall and in correspondence of a thermal bridge due to the presence of a pillar, where the heat flux is two times the one of the wall. Consider 7 W/(m2 K) as heat transfer coefficient on the indoor surface.

(no condensation; yes condensation)

Exercise 6 (2 pts)

Calculate the layer of insulation which is necessary to add to the wall with the given stratigraphy in order to meet the requirements of a building regulation which imposes a U-value lower than 0.21 W/(m2K). Assume a thermal conductivity for the insulation equal to 0.038 W/(m K) and heat transfer coefficient of 25 and 10 for the outdoor and indoor surfaces respectively.

SECOND PART

The underfloor heating system of a building is connected to an air-source heat pump, which provides an heating capacity of 4 kW with a COP of 4 when the outdoor air temperature is -3 °C. Calculate:

-     the mass flow rate of water delivered to the underfloor heating system if the temperature difference between supply and return is 6 °C;

-     the electric power required to power the heat pump and heat duty at the evaporator;

-     the refrigerant mass flow rate, knowing that the  enthalpy of the refrigerant (R134a) at the outlet of the compressor is equal to 290 kJ/kg and the condensing pressure is 10 bar;

-     the isentropic efficiency of the compressor considering that the evaporation temperature is 3 °C lower than the outdoor air temperature.

(0.159 kg/s; 1 kW; 3 kW; 0.022 kg/s; 0.70)