Refrigerant-134a enters the condenser of a residential heat...

Refrigerant-134a enters the condenser of a residential heat pump at $800 \mathrm{kPa}$ and $50^{\circ} \mathrm{C}$ at a rate of $0.022 \mathrm{~kg} / \mathrm{s}$ and leaves at $750 \mathrm{kPa}$ subcooled by $3^{\circ} \mathrm{C}$. The refrigerant enters the compressor at 200 kPa superheated by $4^{\circ}$ C. Determine $(a)$ the isentropic efficiency of the compressor, $(b)$ the rate of heat supplied to the heated room, and $(c)$ the COP of the heat pump. Also, determine $(d)$ the $\mathrm{COP}$ and the rate of heat supplied to the heated room if this heat pump operated on the ideal vapor-compression cycle between the pressure limits of 200 and $800 \mathrm{kPa}$.

Key Concepts

Thermodynamic Properties of Refrigerants

Understanding the thermodynamic properties of refrigerants, such as pressure, temperature, enthalpy, and entropy, is essential for analyzing the performance of refrigeration and heat pump systems. These properties allow engineers to determine state points, evaluate phase changes, and perform energy and mass balance calculations within the vapor-compression cycle, ultimately influencing parameters like work, heat transfer, and efficiency.

Vapor-Compression Cycle

This cycle is the fundamental process used in refrigeration and heat pump systems. It involves the compression of a refrigerant gas, its condensation to a liquid at a high pressure, expansion to a lower pressure, and subsequent evaporation to absorb heat. Understanding this cycle is key to analyzing system performance, assessing energy flows, and calculating quantities like the rate of heat transfer and system efficiency.

Refrigeration Heat Pump

A refrigeration heat pump is a system that transfers heat from a cooler space to a warmer space by using external work, typically through a compressor. In this context, it is designed to deliver heat to a heated room, and its performance is measured by how effectively it can convert input work into heat output, which is evaluated via parameters such as the coefficient of performance (COP).

Isentropic Efficiency

Isentropic efficiency quantifies the performance of a compressor by comparing the actual work input to the ideal work input required for an isentropic (reversible and adiabatic) process. A high isentropic efficiency indicates that the compressor is performing close to its ideal behavior, which is crucial for accurately determining the work required and the overall efficiency of the thermodynamic cycle.

Coefficient of Performance (COP)

The coefficient of performance (COP) is a measure of the efficiency of a heat pump or refrigeration system. It is defined as the ratio of useful heating or cooling provided to the work input. A higher COP indicates a more efficient system, and calculating the COP involves understanding the energy exchanges during compression, condensation, expansion, and evaporation processes in the cycle.

Superheating and Subcooling

Superheating and subcooling refer to the controlled adjustments of the refrigerant's temperature relative to its saturation temperature. Superheating occurs when the vapor is heated above its saturation temperature, which can ensure that the refrigerant remains in a vapor state before entering the compressor. Subcooling occurs when the liquid refrigerant is cooled below its saturation temperature, which prevents vaporization before the expansion process. Both processes are important in managing the quality of the refrigerant and optimizing the performance of the cycle.

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