Thermo.docx

WESLEYAN UNIVERSITY-PHILIPPINES Mabini Extension, Cabanatuan City COLLEGE OF ENGINEERING AND COMPUTER TECHNOLOGY

THERMODYNAMIC CYCLES

SUBMITTED TO: Engr. Elizabeth R. De Leon

SUBMITTED BY: Jean Marie M. Villarico BSECE-4B

Thermodynamic Cycles A thermodynamic cycle is a series of processes where the properties of the system are the same after the cycle as they were prior. Three main properties — temperature, pressure, and specific volume — are tracked when a system undergoes a set of processes. To be considered a cycle, all three properties need to be the same at their initial state and at the end. One property could remain the same throughout any one of processes; the cycle is considered isothermal if temperature is constant, isobaric if pressure is constant, and isochoric or isometric if specific volume is constant. The most efficient type of cycle is one that has only reversible processes, such as the Carnot cycle, which is made up of four reversible processes.

CARNOT CYCLE The Carnot cycle has the greatest efficiency possible of an engine (although other cycles have the same efficiency) based on the assumption of the absence of incidental wasteful processes such as friction, and the assumption of no conduction of heat between different parts of the engine at different temperatures.

The Carnot cycle consists of the following steps: 1. Reversible isothermal expansion of the gas at the "hot" temperature, TH( Isothermal heat addition ). During this step, the expanding gas causes the piston to do work on the surroundings. The gas expansion is propelled by absorption of heat from the high temperature reservoir. 2. Reversible adiabatic expansion of the gas. For this step we assume the piston and cylinder are thermally insulated, so that no heat is gained or lost. The gas continues to expand, doing work on the surroundings. The gas expansion causes it to cool to the "cold" temperature, TC. 3. Reversible isothermal compression of the gas at the "cold" temperature, TC.( Isothermal heat rejection ) Now the surroundings do work on the gas, causing heat to flow out of the gas to the low temperature reservoir. 4. Reversible adiabatic compression of the gas. Once again we assume the piston and cylinder are thermally insulated. During this step, the surroundings do work on the gas, compressing it and causing the temperature to rise to TH. At this point the gas is in the same state as at the start of step 1.

P-V diagram of the Carnot Cycle

T-S diagram of the Carnot Cycle

EXAMPLE PROBLEMS: 1. Carnot engine operates with efficiency of 40 %. How much must the temperature of the hot reservoir increase, so that the efficiency increases to 50 %? The temperature of the cold reservoir remains at 9 °C.

Formula: η=

𝐓𝟏−𝐓𝟐 𝐓𝟏

Where : T1 – temperature of hot reservoir T2 – temperature of cold reservoir

Given values: η = 40 % = 0.4 η = 50 % = 0.5 t = 9 °C => T = 282 K T =? 1

2

2

2

1

Solution: First we write down the relationships for the initial efficiency η1 of Carnot engine and for the efficiency η2 after changing the temperature of the hot reservoir:

where T1 is the initial temperature of the hot reservoir, T1* is the new temperature of the hot reservoir, and T2 is the temperature of the cold reservoir. Now we evaluate the unknown temperatures T1 and T1* from these relations:

The unknown temperature difference ΔT1 of the hot reservoir is given by:

and by substituting the above evaluated temperatures we obtain

The temperature of the hot reservoir must increase by 94 K. 4

2. A Carnot engine operates between 300˚C and 150˚C, absorbing 6.00 × 10 J per cycle at the higher temperature. How much work per cycle is this engine capable of performing? Solution:

OTTO CYCLE The Otto cycle was given by Dr. Nikolaus August Otto. It is a gas power cycle that is used in spark ignition engine (petrol engine) for its working. The entire modern petrol engine works on Otto cycle. It consist of four processes, Two isentropic (reversible adiabatic) processes and two isochoric (constant volume) processes. It has low compression ratio ranges from 7:1 to 10:1. The four processes of this cycle is as follows: 1. Isentropic ( reversible adiabatic) compression 2. Constant volume (Isochoric) heat addition 3. Isentropic (reversible adiabatic) Expansion 4. Constant volume heat rejection.

1. Process 1-2: Isentropic Compression This process involves the motion of piston from TDC to BDC. The air that is sucked into cylinder during suction stroke undergoes reversible adiabatic (isentropic) compression. Since the air is compressed, the pressure increases from P1 to P2, the volume decreases from V1 to V2, temperature rises from T1 to T2, and entropy remains constant. 2. Process 2-3: Constant Volume Heat Addition This process is an isochoric process i.e. the heat is added to the air at constant volume. The piston in this process rest for a moment at TDC and during this time heat is added to the air through external source. Due to the heat addition, the pressure increases from P2 to P3, pressure, volume remains constant (V2=V3), temperature increases from T2 to T3 and entropy increases from S2 to S3. The amount of heat added is given by 3. Process 3-4: Isentropic Expansion In this process, the isentropic (reversible adiabatic) expansion of air takes place. The piston moves from TDC to BDC. Power is obtained in this process which is used to do some work. Since this process involves expansion of air, so the pressure decreases from P3 to P4, volume increases from V3 to V4, temperature falls from T3 to T4 and entropy remains unchanged (S3=S4).

4. Constant Volume Heat Rejection In this process, the piston rest for a moment at BDC and rejection of heat takes place at constant volume. The pressure decreases from P4 to P1, Volume remains constant (V4=V1), temperature falls from T4 to T1. The amount of heat rejected in this process is given by

Thermal Efficiency The efficiency of Otto cycle is given by

Application It is used in all two stroke and four stroke petrol engines of motorcycles, cars, and other light duty vehicles.

Example Problems: 1. The compression ratio of an air-standard Otto cycle is 9.5. Prior to the isentropic compression process, the air is 100 kPa, 35℃, and 600𝑐𝑚3 . The temperature at the end of the isentropic expansion process is 800 K. Using the specific heat values at room temperature, determine a. The highest temperature and pressure in the cycle b. The amount of heat transferred in kJ c. Thermal efficiency d. Mean effective pressure (MEP) Solution:

2. An air standard Otto cycle has a compression ratio of 15. The outside air conditions are 14.7 and the temperature is 560 R. When 1500 btu/lbm is added to the cycle, what is the ideal thermal efficiency?

Ideal thermal efficiency for Otto cycle

Compression Ratio (𝑟𝑣 )= 15 Ratio of Specific Heats for air = 1.4 Solution:

The efficiency is 66.15%