91Ó°ÊÓ

Specific enthalpy is a key concept in thermodynamics that represents the heat content per unit mass of a substance. It's expressed in units of energy per mass, usually \(\text{kJ/kg}\). In this exercise, the specific enthalpy at the inlet and outlet of the pipe was given as \(3200 \text{kJ/kg}\) and \(1900 \text{kJ/kg}\) respectively.

• Inlet Specific Enthalpy: The energy content per kilogram of steam entering the pipe.
• Outlet Specific Enthalpy: The energy content per kilogram of steam exiting the pipe.

The drop in specific enthalpy indicates that the steam loses energy as it passes through the pipe. This energy loss is represented by the rate of heat transfer. Hence, specific enthalpy helps us measure the amount of heat involved in the process.

A steady-flow process implies that the fluid properties within a control volume do not change with time. In simpler terms, the conditions (like pressure, temperature, and specific enthalpy) within the system are constant. For the problem at hand, this means:

• Mass Flow Rate (\( \dot{m} = 0.6 \text{ kg/s} \)): The amount of mass flowing through the pipe per second.
• Energy Flow: The energy associated with the mass flow remains steady.

Since the system operates at steady-state, we disregard any accumulation of energy within the pipe. The calculations revolve around the inlet and outlet conditions. Therefore, understanding that no significant change occurs in kinetic energy allows us to simplify our calculations, focusing primarily on the changes in enthalpy.

The energy balance equation is derived from the First Law of Thermodynamics. It relates the energy entering and exiting a control volume. For a steady-flow process, the energy balance equation is simplified to cover only the relevant parameters. In our case: \[ \dot{Q} = \dot{m} \times (h_{in} - h_{out}) \]
Here, \( \dot{Q} \) is the rate of heat transfer, \( \dot{m} \) is the mass flow rate, \( h_{in} \) is the specific enthalpy at the inlet, and \( h_{out} \) is the specific enthalpy at the outlet.

To determine the heat transfer rate in the problem, we:

• Identified the specific enthalpy values at the inlet and outlet.
• Used the mass flow rate provided.
• Substituted these values into the energy balance equation.

This resulted in: \[ \dot{Q} = 0.6 \text{ kg/s} \times (3200 \text{ kJ/kg} - 1900 \text{ kJ/kg}) \]
Simplifying, we find the heat transfer rate: \[ \dot{Q} = 0.6 \times 1300 = 780 \text{ kW} \] Using the energy balance equation enabled us to determine that the steam loses \(780 \text{ kW} \) of energy to its surroundings as it flows through the pipe.