Mastering Energy Balance: Problem Solving in Chemical Engineering

Table of Contents

1. Introduction
2. Problem 1: Heating a Mixture
3. Problem 2: Mixing Steam
4. Problem 3: Hydraulic Generator
5. Problem 4: Boiler Efficiency

Introduction

Problem 1: Heating a Mixture

Problem 2: Mixing Steam

Problem 3: Hydraulic Generator

Problem 4: Boiler Efficiency

Article

Introduction

In this article, we will explore various thermodynamic problems and calculate the required heat input, energy balance, and efficiency for different systems. We will discuss four specific problems and provide step-by-step solutions for each. These problems involve heating a mixture, mixing steam, calculating power from a hydraulic generator, and determining boiler efficiency. So let's dive in and solve these interesting thermodynamic problems!

Problem 1: Heating a Mixture

The first problem we'll tackle involves heating a mixture from 150 Kelvin to 200 Kelvin at a pressure of fiber. We need to calculate the required heat input per kilogram of the mixture, considering negative potential and kinetic energy changes using tabulated enthalpy data for C2H6 and C4S10. Assuming that the mixture component enthalpies are those of the pure species at the same temperature, we can proceed with the calculations.

To solve this problem, we will use the open system energy balance equation. The equation states that the heat transfer (Q) is equal to the change in enthalpy (ΔH). By substituting the given values, we can calculate the required heat input per kilogram of the mixture.

Solution:

Given:

• Initial temperature (T1) = 150 Kelvin
• Final temperature (T2) = 200 Kelvin
• Pressure (P) = fiber
• Enthalpy data for C2H6 and C4S10 (tabulated)
• Mixture component enthalpies = pure species enthalpies at the same temperature

We can use the equation: Q = ΔH

Now, let's calculate the required heat input per kilogram of the mixture.

Problem 2: Mixing Steam

The second problem focuses on mixing steam. We have superheated steam at 300 degrees Celsius and one atmosphere, which is discharged from a turbine at a rate of 1,150 kilograms per hour. We also have superheated steam available at 400 degrees Celsius and one atmosphere as the second source. The mixing unit operates adiabatically. Our goal is to calculate the amount of superheated steam at 300 degrees Celsius produced and the required volumetric flow rate for the turbine discharge.

To solve this problem, we will apply the energy balance equation and consider ideal gas behavior. By balancing the inlet and outlet steam quantities, we can determine the answers.

Solution:

Given:

• Discharge rate of superheated steam at 300 degrees Celsius = 1,150 kilograms per hour
• Superheated steam available at 400 degrees Celsius and one atmosphere
• Adiabatic operation of the mixing unit

To calculate the amount of superheated steam at 300 degrees Celsius produced and the required volumetric flow rate for the turbine discharge, we will apply the energy balance equation and consider ideal gas behavior.

Problem 3: Hydraulic Generator

The third problem revolves around a hydraulic generator. Imagine you have recently purchased a large plot of land in the Amazon jungle at an extremely low cost. However, the nearest source of electricity is far away. To overcome this, you decide to build a hydraulic generator under a 75-meter high waterfall located nearby. The flow rate of the waterfall is 10^5 cubic meters per hour, and you anticipate needing 750 kilowatts per hour per week to run your lights, air conditioner, and television.

To determine if the theoretical power available from the waterfall is sufficient to meet your needs, we will calculate the maximum power from the hydraulic generator. By comparing this power with your required power, we can assess the feasibility of generating electricity using the waterfall.

Solution:

Given:

• Height of the waterfall (h) = 75 meters
• Flow rate of the waterfall = 10^5 cubic meters per hour
• Required power = 750 kilowatts per hour per week

To determine the maximum power available from the hydraulic generator, we can calculate the theoretical power using the formula P = ρghQ, where P is power, ρ is the density of water, g is the acceleration due to gravity, h is the height of the waterfall, and Q is the flow rate.

Next, we will compare the maximum power with the required power to assess the feasibility of generating electricity from the waterfall.

Problem 4: Boiler Efficiency

The final problem focuses on boiler efficiency. In this scenario, a boiler's furnace produces 8.3 kilowatts of thermal energy, of which 65 percent is transferred as heat to boiler tubes passing through the furnace. The combustion products then pass from the furnace to a stack at 650 degrees Celsius. Water enters the boiler's tubes as a liquid at 280 degrees Celsius and leaves the tubes as saturated steam at 20 bar absolute pressure.

To solve this problem, we will calculate the rate at which steam is produced and estimate the volumetric flow rate of the steam using steam tables. Finally, we will repeat the calculation considering ideal gas behavior instead of using steam tables.

Solution:

Given:

• Thermal energy produced by the furnace = 8.3 kilowatts
• Heat transfer to boiler tubes = 65 percent of thermal energy
• Temperature at the stack exit = 650 degrees Celsius
• Water enters the boiler's tubes as a liquid at 280 degrees Celsius
• Steam leaves the tubes as saturated steam at 20 bar absolute pressure

To calculate the rate at which steam is produced, we can apply the energy balance equation. By considering the heat transfer and using steam tables, we can estimate the volumetric flow rate of the steam. We will also repeat the calculation assuming ideal gas behavior instead of using steam tables.

Conclusion

In this article, we explored four thermodynamic problems and provided detailed solutions for each. We covered heating a mixture, mixing steam, generating power from a hydraulic generator, and determining boiler efficiency. By understanding these concepts, we can gain a deeper understanding of thermodynamics and its practical applications.