In the case of Rankine cycle, the specific volume of water in the pump is __________ of the steam expanding in the same turbine.

Explanation:

Rankine Cycle: Specific Volume of Water in Pump vs. Steam Expanding in Turbine

• The Rankine cycle is a fundamental thermodynamic cycle commonly used in power generation systems, particularly in steam power plants. It consists of four main processes: isentropic compression in a pump, heat addition in a boiler, isentropic expansion in a turbine, and heat rejection in a condenser. One of the critical aspects of the Rankine cycle is the specific volume of the working fluid at different stages of the cycle.

In the Rankine cycle, the working fluid undergoes a phase change during the cycle. Here’s why the specific volume of water in the pump is much less than that of the steam expanding in the turbine:

1. Specific Volume of Water in the Pump:

• The pump handles liquid water (subcooled or saturated) at a low temperature and pressure. Liquid water has a very low specific volume compared to steam.
• The specific volume of liquid water is nearly constant and extremely small, typically in the range of 0.001 m³/kg (depending on the pressure and temperature).
• Since the pump compresses liquid water to a higher pressure, the increase in specific volume during this process is negligible.

2. Specific Volume of Steam Expanding in the Turbine:

• The turbine handles steam, which is either dry saturated or superheated, depending on the operating conditions of the cycle.
• Steam has a significantly larger specific volume than liquid water because it exists in the gaseous phase. For instance, the specific volume of steam can be several hundred times that of liquid water, depending on the pressure and temperature.
• As the steam expands in the turbine, its specific volume increases further due to the drop in pressure. This is a characteristic of the expansion process in the Rankine cycle.

3. Comparison:

• The specific volume of water in the pump is orders of magnitude smaller than the specific volume of steam in the turbine. For example, at a pressure of 1 bar, the specific volume of saturated liquid water is approximately 0.001 m³/kg, while the specific volume of saturated steam is around 1.67 m³/kg—a difference of more than 1000 times.
• This significant difference arises because of the phase change from liquid to vapor and the associated increase in volume during boiling and expansion.