My dad is considering a new heating system for his shop. On a typical winter day it is desirable for the shop to be maintained at an average temperature of 70F and the surroundings are at 20F. Due to this temperature difference, there is a heat transfer out of his shop (it is insulated) of 2500 W. The cost of electricity where my dad lives is 0.06 $/kW-hr. One of his friends is raving about an infrared electric heating system he purchased from a TV show. a.) How much will it cost to continuously heat the shop with the electric system for 30 days. (2 points) I recommended my dad find an old window mounted air conditioning unit. The system can be used to cool the shop in the summer and reversed for heating in the winter. By reversing the system it can be operated as a heat pump, capture heat from the outdoors, and heat the shop at hopefully a much lower cost than the electric system. My dad found a unit that he has decided to try out. I was able to find some information on the air conditioner, specifically the compressor, but not much else. The air conditioner uses R134a. The compressor is driven by an electric motor that spins at 1350 revolutions per minute. The compressor has a displacement of 4.5 in?, an isentropic efficiency of 0.78 and a volumetric efficiency of 0.70. For this quick analysis we'll assume that there is no approach temperature differential or pressure drop in either the evaporator or condenser. Since we can't contact the air conditioner manufacturer to obtain specifics, we'll assume the fluid leaving the evaporator is a saturated vapor and the fluid leaving the condenser is a saturated liquid. b.) Create a state table of your properties for this problem. The evaporator is between states 1 and 2, the compressor between 2 and 3, the condenser between 3 and 4, and the throttle between 4 and 1. Include the following properties in your table: Temperature, Pressure, quality, volume, enthalpy, and entropy. (4 points) c.) Plot a T-s diagram of the cycle showing your four points above overlayed on the vapor dome and arrows indicating the direction of the cycle. (4 points) d.) What is the Volumetric flow rate (m^3/s) and mass flow rate (kg/s) of refrigerant into the compressor? (4 points) e.) What is the electrical work required to drive the compressor (assuming no electric motor losses) and the heat provided to the shop from the condenser at these conditions? (6 points) f.) Estimate the Coefficient of Performance (COP) for the air conditioner when operated as a heat pump at the design conditions between the shop temperature and the outdoor temperature. How does this value compare to the Carnot COP of an ideal heat pump operating under the same conditions? (2 points) g.) What is the cost to operate the heat pump for 30 days? (2 point) My dad is considering a new heating system for his shop. On a typical winter day it is desirable for the shop to be maintained at an average temperature of 70F and the surroundings are at 20F. Due to this temperature difference, there is a heat transfer out of his shop (it is insulated) of 2500 W. The cost of electricity where my dad lives is 0.06 $/kW-hr. One of his friends is raving about an infrared electric heating system he purchased from a TV show. a.) How much will it cost to continuously heat the shop with the electric system for 30 days. (2 points) I recommended my dad find an old window mounted air conditioning unit. The system can be used to cool the shop in the summer and reversed for heating in the winter. By reversing the system it can be operated as a heat pump, capture heat from the outdoors, and heat the shop at hopefully a much lower cost than the electric system. My dad found a unit that he has decided to try out. I was able to find some information on the air conditioner, specifically the compressor, but not much else. The air conditioner uses R134a. The compressor is driven by an electric motor that spins at 1350 revolutions per minute. The compressor has a displacement of 4.5 in?, an isentropic efficiency of 0.78 and a volumetric efficiency of 0.70. For this quick analysis we'll assume that there is no approach temperature differential or pressure drop in either the evaporator or condenser. Since we can't contact the air conditioner manufacturer to obtain specifics, we'll assume the fluid leaving the evaporator is a saturated vapor and the fluid leaving the condenser is a saturated liquid. b.) Create a state table of your properties for this problem. The evaporator is between states 1 and 2, the compressor between 2 and 3, the condenser between 3 and 4, and the throttle between 4 and 1. Include the following properties in your table: Temperature, Pressure, quality, volume, enthalpy, and entropy. (4 points) c.) Plot a T-s diagram of the cycle showing your four points above overlayed on the vapor dome and arrows indicating the direction of the cycle. (4 points) d.) What is the Volumetric flow rate (m^3/s) and mass flow rate (kg/s) of refrigerant into the compressor? (4 points) e.) What is the electrical work required to drive the compressor (assuming no electric motor losses) and the heat provided to the shop from the condenser at these conditions? (6 points) f.) Estimate the Coefficient of Performance (COP) for the air conditioner when operated as a heat pump at the design conditions between the shop temperature and the outdoor temperature. How does this value compare to the Carnot COP of an ideal heat pump operating under the same conditions? (2 points) g.) What is the cost to operate the heat pump for 30 days? (2 point)
