Diesel Engine and Entropy and Disorder

Diesel Engine

The engine was designed by Rudolf Diesel in 1892 who was dissatisfied with the low efficiency of the Otto engine and began to investigate to increase its efficiency. In the diesel engine, air is working substance and diesel is fuel. This engine works on the four –stroke engine.

1. Suction stroke
   Air valve I is opened and pure sir at atmospheric pressure are drawn into the cylinder by the outward motion of the piston as shown in the figure.
2. Compression stroke
   All the valves are closed, as the piston start moving inwards as in the figure. Air is compressed adiabatically to about 1/17^th of its initial volume by the inward motion of the piston. In this process, the temperature is raised to about 1000^o
3. Working stroke
   The oil valve O is opened and diesel oil is forced in under pressure as shown in the figure. At high temperature, the oil burns spontaneously. The supply of oil is so regulated that during combustion, as the piston moves forward, the pressure remains constant. In this process, the burning fuel supplies heat to the air at constant pressure. At a certain stage when the temperature has reached the maximum value, about 2000 K, the supply of oil is cut off. This is the stroke in which useful work is done.
4. Exhaust stroke
   As the piston moves inwards, exhaust valve E is opened and the useless gas mixture is forced out of the cylinder as shown in the figure.
   

   

The diesel cycle on a P-V diagram

The PV-diagram for an ideal diesel cycle as shown in the figure. The portion EC represents the isobaric suction stroke. At point C the cylinder is full of air at volume V₁ and atmospheric pressure. The portion CD represents the adiabatic compression stroke. At point D the volume V₂ is 1/17 that of the volume V₁. The portion DA represents the quasi-static isobaric burning of oil. During this process of Q₁ amount of heat is absorbed. The volume at A is V₃ and the temperature about 2000 K. At point A the supply of fuel is cut off and the remaining part of working stroke is represented by adiabatic expansion AB. At B the exhaust valve is opened so that the pressure drops to C, the atmospheric pressure. During the process BC, Q₂ amount of heat is rejected to the surroundings, the portion CE represents the exhaust stroke in which useless gas mixture is forced out. At E out let valve O closes and inlet valve I is open. Then the cycle again starts.

Efficiency of a Diesel Engine

Suppose Q₁ be the amount of heat absorbed by the working substance at a constant pressure during combustion DA. Let Q₂ be the amount of heat rejected at the constant volume during the release of heat BC. Then the efficiency is given by
\begin{align*} \eta &= 1 - \frac {Q_1}{Q_2} \\ &= 1 - \left (\frac {1}{\gamma } \right )^{\rho -1} \\ \text {where,} \: \rho = V_1/ V_2 \: \text {is called compression ratio} \\\end{align*}

Merits and Demerits of Diesel of Engine

A diesel engine has higher efficiency than that of a petrol engine. As the diesel is less inflammable than petrol, it has less risk of firing. Its reliability is greater than that of a petrol engine. Diesel oil is cheaper than petrol so the running expense is less than a petrol engine.

The diesel engine is heavier than the petrol engine, so it could not be used in light vehicles like aeroplanes, scooter etc.

Distinguish between Petrol and Diesel Engine

Entropy and Disorder

Entropy is a measure of the disorder of a system. The change in entropy, dS, when a system changes from one equilibrium state to another is defined, where dQ is the amount of heat added to the system or subtracted from the system or subtracted from the system and T is the absolute temperature of the system.

1. If heat, dQ is added to the system, then dQ is positive and hence entropy of the system increases.
2. If dQ is subtracted from the system, then dQ is negative and hence entropy of the system decreases.

Whenever a physical system is allowed to distribute its energy freely, disorder increases i.e. entropy increases. For example, suppose you have a box with a partition dividing it in two, with a gas on one side of the partition and other side evacuated as shown in the figure. With all the molecules of gas on one side, gas has a highly ordered situation. However, if the partition is removed as shown in the figure, the gas molecules will distribute themselves throughout the box and be moving in random directions. We say that entropy of gas has increased because the amount of disorder has increased. As the disorder of system increases, its entropy increases. In order to change the disordered system to the ordered one, some work will have to be done.

Kelvin temperature Scale

Suppose a reversible engine takes in a quantity of heat Q₁ at temperature T₁ and rejects a quantity of heat Q₂ at temperature T₂. Then

$$ \frac {Q_1}{Q_2} = \frac {T_1}{T_2} \dots (i) $$

This equation defines Kelvin temperature scale i.e absolute temperature scale. The ratio of any two temperatures on this scale is equal to the ratio of heats absorbed and rejected by a Carnot reversible engine working between two temperatures.
Equation (i) can be written as
$$\frac {Q_1 –Q_2}{Q_1} = \frac {T_1 –T_2}{T_1} $$

Since Q₁ – Q₂ represents the work done W per cycle by the reversible engine operating between the two temperature T₁ and T₂, the temperature is measured in terms of work and hence this scale is also known as work scale of temperature.