A vacuum pump operates by compressing gases from a closed...

A vacuum pump operates by compressing gases from a closed chamber to atmospheric pressure in order that these gases can be ejected to the atmosphere. A vacuum drier operating at $700 \mathrm{~mm}$ $\mathrm{Hg}$ vacuum (atmmospheric pressure is $760 \mathrm{~mm} \mathrm{Hg}$ ) and $50^{\circ} \mathrm{C}$ generates $500 \mathrm{~g}$ of water vapor per minute by evaporation from a wet material in the dryer. In addition, the leakage rate for ambient air infiltrating the dryer is estimated to be $1 \mathrm{~L} / \mathrm{h}$ at $1 \mathrm{~atm}$ and $20^{\circ} \mathrm{C}$. (a) Calculate the total volume of gases that must be removed by the vacuum pump per minute. (b) If the pump compresses the gas in an adiabatic process, calculate the theoretical horsepower required for the pump. The specific heat ratio for water is 1.30 , and that for air is 1.40 .

A vacuum pump operates by compressing gases from a closed chamber to atmospheric pressure in order that these gases can be ejected to the atmosphere. A vacuum drier operating at $700 \mathrm{~mm}$ $\mathrm{Hg}$ vacuum (atmmospheric pressure is $760 \mathrm{~mm} \mathrm{Hg}$ ) and $50^{\circ} \mathrm{C}$ generates $500 \mathrm{~g}$ of water vapor per minute by evaporation from a wet material in the dryer. In addition, the leakage rate for ambient air infiltrating the dryer is estimated to be $1 \mathrm{~L} / \mathrm{h}$ at $1 \mathrm{~atm}$ and $20^{\circ} \mathrm{C}$.
(a) Calculate the total volume of gases that must be removed by the vacuum pump per minute.
(b) If the pump compresses the gas in an adiabatic process, calculate the theoretical horsepower required for the pump. The specific heat ratio for water is 1.30 , and that for air is 1.40 .

Key Concepts

Mechanical Work and Horsepower in Compression Systems

Calculating the mechanical work involved in compressing a gas is critical for assessing the energy requirements of pumps and compressors. This work is often related to the power output in horsepower. Converting the thermodynamic work into mechanical power involves considering both the thermodynamic efficiency of the process and the specific process conditions, such as the adiabatic nature of the compression.

Ideal Gas Law and Gas Volume Calculations

The ideal gas law (PV = nRT) is used to relate the pressure, volume, and temperature of a gas. This fundamental principle is crucial for converting between different states and conditions of a gas. It allows one to calculate the volume of gas at specific pressures and temperatures, which is particularly important when determining the total volume that a pump must remove from a system.

Vacuum Pump Operation

This concept involves the mechanism by which a vacuum pump reduces the pressure within a closed chamber by removing gases. In many industrial applications, it is used to create a controlled environment, remove unwanted gases, or assist in processes such as drying. The overall efficiency and design of the pump depend on accurately determining the volume of gases that must be handled under varying operational conditions.

Adiabatic Compression

Adiabatic compression refers to the process in which a gas is compressed without any heat exchange with the surrounding environment. This leads to a rise in temperature and requires calculation of work based on the specific heat ratio (gamma) of the gas. Understanding adiabatic processes is essential in thermodynamics, particularly when designing compressors, as it directly impacts the energy and power requirements of these devices.

Transcript

00:02 Hello friends, in this problem it is given an air pump having a cylinder of length.

00:11 .25 meter with movable piston.

00:16 The pump is used to compress here from atmospheric pressure.

00:21 Initial pressure is atmospheric into a very large tank of pressure.

00:39 4 .2 pascal.

00:46 Specific heat of air is given 20 .8.

00:51 Jule per kg per kelvin in the first part we have to find the distance moved by the piston so that air enter into the tank in b part we have to find the temperature of compressed air that is t2 in c part we have to calculate work done let us see here we start solving with first part initial volume will be a into h1 and final volume is a into h2 using adiabetic relation to find the air to enter.

01:53 So we can use pressure into volume to the power gamma to be constant.

02:02 From here you may write v2 is called to v1, p1 upon p2 to the power 1 upon gamma, b1 is a into h2, b1 is a into h1, p1 is one atmospheric pressure and p2 is this is the gorge pressure of the tank, this is not the actual pressure, this is the gorge pressure is given.

02:40 So actual pressure will be atmospheric pressure to be added.

02:45 So it becomes 4 .5 .21 into 10 to the power 5 pascal.

02:53 On solving it h1 we know so we can find h2 so from here h2 is h1 that is 0 .25 and gamma is 1 upon 1 .4 so on solving it this will be 1 .101 upon 521 to the power 1 upon 1 .4 so on solving it h2 you will get 0774 million distance moved by the piston is called to h1 minus h2 h1 is 0 .25 meter and h2 is 0 .0774 meter...

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