# Calculating work of Otto cycle stages - Thermodynamics.

• Pull and Twist
In summary, the Otto cycle is a cycle used in automobiles that consists of an adiabatic compression (the cylinder compresses), isochoric compression (the fuel ignites, increasing the temperature in too short a time for the piston to move), adiabatic expansion (the cylinder expands), and isochoric expansion (exhaust gas let out, fresh air and fuel let in.) The cycle is efficient, with a temperature of the released gas that is determined by the amount of heat added to the system during combustion.
Pull and Twist
One big coincidence of thermodynamics is that automobiles are usually powered by an Otto cycle This cycle consists of an adiabatic compression (the cylinder compresses), isochoric compression (the fuel ignites, increasing the temperature in too short a time for the piston to move), adiabatic expansion (the cylinder expands), and isochoric expansion (exhaust gas let out, fresh air and fuel let in.)

In a particular engine, a starts by taking in 1000cm3 of air (p=1.2kg/m3). Next, an amount of fuel is added equivalent to 1% of the mass of the air in the piston (since gasoline is composed of large molecules, assume that this does not affect the pressure in the piston). The piston is then compressed to a volume of 100cm3. This compression can be assumed to be adiabatic with PV1.3 being constant. Next, the fuel is ignited, releasing an energy of 45000J for every gram of fuel in the form of heat, while the piston stays at constant volume. You may assume that the heat capacity at constant volume for this gas is 800J/kg*K. After combustion, the piston expands back to the original volume of 1000cm3 adiabatically, and the gasses are released.

1) What is the work required to compress the gas during compression, work done by the gas during the expansion, and total work done during the cycle.?

2) How much heat is added to the system during the combustion stage?

Hint: You may want to answer questions 1&2 together in the form of a U table

3) What is the efficiency of this particular cycle?

4) What is the temperature of the released gas?

Equations we have learned in this section...

PV=NKBT
W=PV
E=Q - W
E=CvT

Was told to utilize google for any other equations or constants that may be useful...

This is how I started working stuff out... but have no idea what I'm actually doing.

How did you get this expression for the work done in the adiabatic step 1→2? It doesn't look quite correct to me. Is the factor of (1-γ) in the right place?

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## 1. What is the Otto cycle and why is it important in thermodynamics?

The Otto cycle is a thermodynamic cycle that describes the idealized process of a four-stroke internal combustion engine. It is important in thermodynamics because it allows us to analyze and understand the performance of these engines and their efficiency.

## 2. How do you calculate the work done in each stage of the Otto cycle?

The work done in each stage of the Otto cycle can be calculated using the formula W = P(V2 - V1), where W is the work done, P is the pressure, and V2 and V1 are the volume at the end and beginning of the stage, respectively. This formula applies to both the compression and expansion stages of the cycle.

## 3. What factors affect the work done in the Otto cycle?

The work done in the Otto cycle is affected by several factors, including the compression ratio, the specific heat ratio of the working fluid, and the temperature at the end of the compression stage. These factors can impact the efficiency and performance of the engine.

## 4. How does the work done in the Otto cycle compare to the actual work done in an internal combustion engine?

The work done in the Otto cycle is an idealized representation of the work done in an internal combustion engine. In reality, there are many factors that can affect the actual work done, such as friction and heat loss. Therefore, the work calculated in the Otto cycle may not be an accurate representation of the actual work done in an engine.

## 5. Can you use the Otto cycle to calculate the efficiency of an internal combustion engine?

Yes, the efficiency of an internal combustion engine can be calculated using the Otto cycle. The efficiency is given by the formula η = 1 - (1/r)^((γ-1)/γ), where r is the compression ratio and γ is the specific heat ratio of the working fluid. This formula can be used to compare the efficiency of different engines or to determine the optimal compression ratio for a given engine.

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