91影视

Saturated steam at \(300^{\circ} \mathrm{C}\) is used to heat a countercurrently flowing stream of methanol vapor from \(65^{\circ} \mathrm{C}\) to \(260^{\circ} \mathrm{C}\) in an adiabatic heat exchanger. The flow rate of the methanol is 6500 standard liters per minute, and the steam condenses and leaves the heat exchanger as liquid water at \(90^{\circ} \mathrm{C}.\) (a) Calculate the required flow rate of the entering steam in \(\mathrm{m}^{3} / \mathrm{min}\). (b) Calculate the rate of heat transfer from the water to the methanol ( \(\mathrm{kW}\) ). (c) Suppose the outlet temperature of the methanol is measured and found to be \(240^{\circ} \mathrm{C}\) instead of the specified value of \(260^{\circ} \mathrm{C}\). List five possible realistic explanations for the \(20^{\circ} \mathrm{C}\) difference. 7 An adiabatic heat exchanger is one for which no heat is exchanged with the surroundings. All of the heat lost by the hot stream is transferred to the cold stream.

Step by step solution

01

Calculate the enthalpy of methanol at the inlet and outlet

Using the specific heat of methanol, calculate the change in enthalpy of methanol per kg between the inlet and outlet temperatures. The specific heat of methanol, \(c_p\) is approximately 2.51 kJ/kg.K. The change in enthalpy, \(螖H_{methanol}\), would be given by \(c_p 脳 螖T_{methanol}\)

02

Calculate the mass flow rate of methanol

The mass flow rate of methanol can be calculated using its flow rate and the density of methanol at standard conditions, which is approximately 0.796 kg/m鲁. Therefore, \(m_{methanol} = 蟻_{methanol} 脳 Q_{methanol}\)

03

Calculate the required flow rate of the entering steam

The heat transferred to the methanol, which is equal to the heat lost by the steam, can be obtained by \(\dot{Q} = m_{methanol} 脳 螖H_{methanol}\). The loss in enthalpy of the steam, \(螖H_{steam}\), that is the difference in enthalpy between the entering and exiting steam, could be obtained from the steam table. Thereafter, the mass flow rate of the steam, \(m_{steam}\), can be calculated using the relation \(\dot{Q} = m_{steam} 脳 螖H_{steam}\). The volumetric flow rate of the steam is obtained by \(Q_{steam} = m_{steam} / 蟻_{steam}\), where \(蟻_{steam}\) is the density of the steam that can be obtained from the steam table.

04

Calculate the rate of heat transfer from the water to the methanol

The rate of heat transfer, \(Q_{heat transfer}\), is obtained directly from Step 3 as the heat loss by the steam, which is equal to the heat gained by the methanol. This is given by \(Q_{heat transfer} = \dot{Q}\).

05

List possible reasons for the difference in outlet temperature

The possible reasons could include, but not limited to: 1) Heat loss to surroundings despite the heat exchanger being adiabatic. 2) Inaccurate measurements of temperatures. 3) Variation in properties from standard values assumed. 4) Internal heat generation in the methanol due to possible reactions. 5) Accumulation of heat within the heat exchanger due to inefficient heat transfer.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Enthalpy Calculations

Enthalpy is a measure of the total energy within a substance, including both internal energy and the energy required to make room for the substance by displacing its environment. In this context, enthalpy calculations are critical to understand how much heat energy is required to change the temperature of methanol vapor in an adiabatic heat exchanger.
First, we need to calculate the change in enthalpy for the methanol vapor as it heats from its initial temperature of 65掳C to its final temperature of 260掳C using its specific heat capacity, which is approximately 2.51 kJ/kg.K. The formula used is:

• \[\Delta H_{methanol} = c_p \times \Delta T_{methanol}\]

where \(\Delta T_{methanol} = 260^{\circ} \mathrm{C} - 65^{\circ} \mathrm{C}\). This enthalpy change must be matched by the heat transferred from the condensing steam, to ensure the methanol reaches the desired temperature.

Methanol Vapor Heating

Methanol vapor heating involves raising the temperature of methanol from an initial lower temperature to a higher target value. This process occurs within an adiabatic heat exchanger, where the heat required for methanol's temperature change is sourced entirely from the condensing steam.
Adiabatic heat exchangers are designed to minimize heat exchange with their surroundings, focusing solely on the heat transfer between the two fluids inside. Methanol in gaseous form begins at a temperature of 65掳C and should ideally be heated to 260掳C. Knowing the flow rate of methanol is 6500 standard liters per minute, we must first determine the mass flow rate of methanol based on its density, roughly 0.796 kg/m鲁, using:

• \[m_{methanol} = \rho_{methanol} \times Q_{methanol}\]

With the mass flow rate known, we can use the enthalpy change calculation to determine the total heat energy required for this heating process.

Steam Condensation

Steam condensation is the process where steam loses heat and changes its phase from vapor to liquid. This phase change involves the release of a significant amount of energy known as latent heat. In the heat exchanger, the role of steam is to give off this energy to the methanol to facilitate its heating.
The steam enters the heat exchanger at a saturated state and 300掳C. It then condenses and exits as liquid water at 90掳C. To understand how much steam is required, we must calculate the decrease in steam enthalpy as it cools and condenses, known as \( \Delta H_{steam} \).
The mass flow rate of steam, \( m_{steam} \), is determined by setting the heat transfer to methanol equal to the heat loss by steam:

• \[\dot{Q} = m_{steam} \times \Delta H_{steam}\]

Steam tables provide necessary enthalpy values to calculate \( \Delta H_{steam} \). The steam's volumetric flow rate can then be deduced using its density.

Heat Transfer Rate

The heat transfer rate in this setup refers to the speed at which heat energy is moved from the steam to the methanol. Understanding the rate of heat transfer, \( Q_{heat transfer} \), is crucial in achieving the desired final temperature for methanol without energy losses.
The heat transfer rate can be calculated using the mass flow rates and enthalpy changes derived in previous steps:

• \[Q_{heat transfer} = \dot{Q} = m_{methanol} \times \Delta H_{methanol} = m_{steam} \times \Delta H_{steam}\]

In practical scenarios, a discrepancy in not reaching the anticipated outlet temperature of methanol could result from inaccuracies in temperature measurement, potential heat losses, or deviations in the thermodynamic properties of the fluids. Identifying and resolving these issues is essential to ensure optimal and efficient heat exchange in the system.