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# Thermodynamics and Engines

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Thermodynamics, which deals with how work and energy (heat) are produced and consumed, is used to model engines. Thermodynamics allows us to ignore the complexities of the mechanical system and concentrate on the engine's input and output instead. The laws of thermodynamics determine the maximum efficiency of a heat engine and how work and energy are related.

At this point, it is important to talk about systems, which in physics can mean an object, a machine, or a living being. A system is anything that can take inputs and respond with outputs. A system's complexity can vary from an ice cube melting in water to a combustion engine or a power plant. Systems can be living beings or non-living objects; they can be as small as gas particles mixing in a room or as large as a planet and all its energy processes.

## Thermodynamic systems

Any system that is surrounded by a boundary and in which energy exchanges occur is a thermodynamic system.

Anything can be a thermodynamic system, from the human body to the sun. Thermodynamic systems are useful to analyze energy and mass exchanges, without taking into account the details of all processes.

### Thermodynamics and Engines: Heat

Heat is the thermal energy transferred to a system or an object. Heat energy exchange is usually described as a thermal change. The change of thermal energy is related to the kinetic energy of the particles that compose substances. The increase in kinetic energy is easily observed in liquids and gases.

Figure 1. Heat is the kinetic energy of the particles composing an object or substance. The particles on the left (T1) have more kinetic energy and, therefore, a higher temperature, Camacho - StudySmarter Originals

### Thermal energy and the internal energy of a gas

The thermal energy of an object is the energy of its molecules or atoms. Thermal energy is the kinetic energy of its particles moving randomly. Higher the kinetic energy, the higher the thermal energy of the object.

The potential energy is the energy stored in the gas molecules. It is composed of the kinetic energy of the gas individual molecules and disordered movement, as also the potential energy between the molecules that compose it and uses the symbol "U".

The kinetic and potential energy should not be confused with the kinetic and potential energy of the gas as a whole.

## Thermodynamics and Engines: Laws of thermodynamics

Thermodynamics has several important laws that describe how a system behaves when work, heat, and entropy change. These laws are universal, and every object in the universe follows them. There are four laws of thermodynamics:

• The zeroth law: the law of thermal equilibrium.
• The first law: the law that describes the internal energy of a substance.
• The second law: the entropy law of irreversibility.
• The third law: the law that states that at zero kelvin, entropy reaches a constant value.

### The zeroth law of thermodynamics

The zeroth law of thermodynamics says that 'two objects or systems are in thermal equilibrium (at the same temperature) if both are in equilibrium with a third object or system'.

For example, when you remove two cupcakes from the oven, taking one out a minute after the other, they will have different temperatures: T1 and T2. The kitchen air, T3, will be different again.

After some time, having cooled down, the temperature of the cupcakes will be the same as that of the kitchen: T1 = T3 and T2 = T3.

The cupcakes have therefore reached the same temperature (T1 = T2) or a "thermal equilibrium".

### The first law of thermodynamics

The first law of thermodynamics says that 'the energy of an object or system that is isolated remains constant' and that 'the energy in the system can be transformed but not destroyed '.

This can be expressed by the following formula:

$∆U=Q-W$

Here ΔU is the change in the object's energy or 'internal energy', while ' W ' and ' Q ' are the heat and the work consumed or produced by the object.

This law is an energy conservation law, as the energy of an object will change only if the object produces or receives work or radiates or obtains heat.

For example, when you heat water in the oven, the internal energy of the water will increase as the molecules start moving faster. This increase is caused by the heat of the oven. In this case, the water does not produce any work.

### The second law of thermodynamics

The second law of thermodynamics specifies the direction in which energy flows. The German scientist Rudolf Clausius wrote,

Heat can never pass from a colder object to a warmer object if no other process intervenes.

We are all used to heat escaping when we open the window on a cold day or the oven door after baking. Less intuitively or logically, however, machines that produce work are unable to convert 100% of the fuel into work. The implications of the second law of thermodynamics are as follows:

• A machine or system always experiences a non-recoverable heat loss.
• The loss of heat or energy is part of an ' irreversible process ', which is to say that it cannot be reversed without using more energy.
• This irreversibility is measured by a variable called entropy, whose symbol is 'S'.

### The third law of thermodynamics

The third law of thermodynamics links the temperature of a system with the atomic order of the system and its energy and says that 'the entropy of a system at zero absolute is constant'. In this case, the entropy of the system is its disorder.

Think of a volume of water at 120 degrees at sea level. At this temperature, water has turned into a gas, and its entropy is high, as the water molecules move freely with high kinetic energy.

When the water temperature decreases to below 100 degrees, the disorder of the water molecules is reduced. The water is liquid again, and its molecules are linked together by stronger forces. Water in this state has less kinetic energy compared to its gas state.

When the temperature decreases to below 0 degrees, the molecules have even less kinetic energy, and their disorder is reduced further, as the particles arrange in a crystal form. Molecules cannot move freely in this state.

When the water is at the lowest known temperature of zero kelvin (or the absolute zero, which is -273.1459 Celsius), its molecules cannot move at all anymore, and the crystals have reached the state of the least possible disorder.

In this process, the disorder of the particles is reduced by extracting energy from the water. As the disorder decreases, the entropy also decreases until it reaches a state where it cannot decrease any further, thus becoming constant.

## What are engines?

In thermal engineering, engines are machines that use thermal energy to produce work or use work to modify the system's thermal energy.

A machine that uses work 'W' to change a system's energy is a cooling or heating machine. A machine that uses heat 'Q' to produce work is a thermal engine or heat engine.

We can see some examples below:

• An air conditioning system is a cooling machine, which uses electrical energy to pass the air of the room through a series of tubes containing a liquid or gas that absorbs the heat of the air, releasing it out of the room.
• A combustion engine in a car is a thermal engine, as it uses gas and an electrical spark to produce a controlled explosion that generates energy and heat. The energy of the explosion is transformed into movement using the car's mechanical components. This movement of the car is what we call 'work'.

See also the following diagrams of a cooling machine (left) and a heat engine (right):

Figure 2.- Examples of thermodynamic machines: The freezer (left) uses energy 'Q' to produce work 'W', which extracts heat from inside the freezer, thus lowering its temperature. The heat engine (right) uses heat from a heat reservoir to produce work, which is converted into energy. Source: Manuel R. Camacho for StudySmarter.

## Thermodynamics and Engines: Efficiency of an engine

Efficiency concerns the amount of work done with the energy used. When more energy is required to do the same amount of work, the engine is less efficient. When less energy is required, the engine is more efficient. As we can measure the energy used in heat units (joules or calories), the efficiency of an engine can be expressed as follows:

$\eta =\frac{W}{Q}$

Here ' W ' is the work done by the machine in joules, while ' Q ' is the energy used by the machine, also in joules. Regarding the efficiency of an engine, note that:

• Efficiency has no units and is known as dimensionless.
• The minimum efficiency for any work done is 0.
• Efficiency cannot be larger than 100%.

We can also calculate a thermal efficiency that is equal to the difference between heat input 'Qin' and heat output 'Qout':

$\eta =\frac{{Q}_{in}-{Q}_{out}}{{Q}_{in}}$

The difference between the heat input and output is the work done by the engine:

$\eta =\frac{W}{{Q}_{in}}$

In the following calculations, the work and heat are both given in joules:

Calculate the efficiency of a machine that produces 134.5 J of work while consuming 340 J of electrical energy, we need to divide the work done by the electrical energy used:

$\eta =\frac{134.5}{340}=0.40$

To obtain the efficiency as a percentage figure, we then need to multiply the result by 100:

$\eta =40%$

Another example is the calculation of the efficiency of an engine that, for instance, heats water from an initial temperature to the desired one. In this case, we begin with the heat equation to determine the amount of energy used to achieve this:

$Q=m·{c}_{p}\left({T}_{i}-{T}_{f}\right)$

Here, 'm' is the mass of water changing its temperature, 'cp' is a variable called specific heat of water at constant pressure, and Tf and Ti are the temperatures final and initial temperatures respectively.

Let's say that, on a moderately cold day, the shower increases the temperature of 1/4 liter (kg) of water from 10 to 22 degrees each second. If the value of cp for water is 4.18 [kj / kgºC] and the device uses 30 kilowatts per second, we can calculate the efficiency of the shower as follows:

$Q=m·{c}_{p}\left({T}_{f}-{T}_{i}\right)=0.25kg·4.18kj/kg{}^{o}C·\left(22-10\right){}^{o}C$

$Q=12.54kj$

The shower using 30 kilowatts per second equates to it using 30kj per second. Applying the energy efficiency formula, we, therefore, get the following:

$\eta =\frac{12.54·{10}^{3}j}{30·{10}^{3}j}=0.418$

Multiplied by 100, the efficiency of the shower is 41.8%.

## Thermodynamics and Engines: Thermodynamic cycles

A thermodynamic cycle is a series of processes performed by a thermal engine that involve heat and work. A thermodynamic cycle is a system in which four variables change: the volume ' V ', the pressure 'P ', the entropy ' S ', and the temperature ' T '. The changes are the result of changes in the internal energy, the work produced or received, or the heat produced or received. Examples of thermodynamic cycles include:

• Carnot cycle.
• Otto cycle.
• Stirling cycle.
• Ericsson cycle.
• Rankine cycle.
• Diesel cycle.
• Brayton cycle.

Each cycle is composed of four steps: compression of a fluid, heat addition to the fluid, expansion of the fluid, and heat rejection by the fluid.

## Thermodynamics and Engines (A2 Only) - Key takeaways

• Thermodynamics is the area of physics that studies energy exchanges where heat and work are involved.
• Thermodynamics and heat engines are related, as engines in thermal engineering are machines that use heat to produce work.
• Engines are also machines that can alter the energy of a system using mechanical work.
• There are four laws of thermodynamics that specify how energy exchanges occur in every system.

It is used to model engines, as thermodynamics deals with how work and energy are consumed and produced.

The laws of thermodynamics determine the maximum efficiency of a heat engine and how work and energy are related.

Efficiency is the amount of work done with the energy used.

Yes, a car engine is a machine that produces mechanical work using fuel in a process that also produces heat.

## Final Thermodynamics and Engines Quiz

Question

What is thermodynamics?.

Thermodynamics is the area of physics that studies energy exchanges where heat and work are involved.

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Question

What is heat?.

Heat is the thermal energy transferred to a system or an object.

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If the temperature of particles composing a liquid or gas increases, does their kinetic energy increase or decrease?

The kinetic energy increases.

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How many thermodynamic laws are there?

Four.

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The first law of thermodynamics involves three concepts that use the symbols ΔU, W, and Q. What do they refer to?.

Internal energy, work, and heat

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If a machine is used to cool down a space, such as a freezer, is this machine a heat engine?.

Yes, it is.

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How does a freezer cool down its interior?.

By extracting heat from the inside to the outside.

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What is efficiency?.

Efficiency is the amount of work done with the energy used.

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If the energy needed to produce work increases but the amount of work done stays the same, does the efficiency increase or decrease?.

The efficiency decreases.

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Does efficiency have a unit?.

No, it is dimensionless.

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What is the minimum efficiency?.

0.

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Can a device reach an efficiency of 100%?.

No, it cannot.

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Calculate the efficiency of a machine that produces 122 joules of work while consuming 560 joules of heat. Hint: use the efficiency equation.

21.7%.

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If a machine has an efficiency of 15% and produces work equal to 3.4[kj], how much energy does it consume? Hint: use the efficiency equation and solve for the heat Q.

813.3 joules.

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What is a thermodynamic cycle?.

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Question

Your electrical coffee machine heats the water from 5 degrees to 55 degrees, using 40 kilowatts of power per second to heat up 50[ml] of water. If the cp constant is 4.18[kj/kgºC], what is the efficiency of the coffee machine?.

Hint: use the heat equation to calculate the power and convert to heat to then use it and divided it by the heat consumed by the machine.

26%

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Question

What is the study of thermodynamics?

It is a branch of physics that studies the behaviour of energy, heat, and the temperature of matter.

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What is the equation of the first law of thermodynamics?

ΔU = ΔQ - ΔW

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How many fundamental laws of thermodynamics are there?

3.

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From which fundamental principle is the first law of thermodynamics derived?

The conservation of energy.

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Who discovered the first law of thermodynamics?

William Rankin and Rudolf Clasius.

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What is the internal energy in a system?

It is the sum of stored kinetic and potential energy of a system.

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What is heat (Q)?

It is the energy transferred by molecular motion and collisions due to a temperature difference.

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What is work (W)?

It is the energy transfer from one system to another.

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What is a closed system?

A closed system exchanges only energy but not matter.

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What is an open system?

A system that exchanges both energy and matter.

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What is an isolated system?

A system that does not have any interactions with its surroundings.

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What type of system is the following example: heating a saucepan on the stove with a lid on?

A closed system that exchanges energy, while the mass remains constant.

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What type of system is the following example: heating a saucepan on the stove with no lid on?

An open system, as it exchanges both energy and mass.

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What type of system is the following example: an ideal thermos containing a hot liquid?

An isolated system can be assumed to have constant energy and mass, and no external interactions.

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Question

Energy is added to a gas, causing it to expand at a pressure of 30 000 Pa from 0.3m3 to 0.6m3. How much work was done on the gas?

W=p DV= 30000(0.6-0.3)= 9000J.

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What are engine cycles?

Four stages in an internal combustion engine that complete a cycle .

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What is the sequence of events in a four stroke engine cycle?

intake,compression, combustion,expansion and exhaust.

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What are two types of engines and what is their operation principle ?

Petrol engine operates under Otto cycle principle

Diesel engine operates under Diesel cycle.

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What of the following conditions is not a condition for otto cycle?

Combustion is isobaric.

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Which of the following conditions is a condition of the ideal otto cycle?

Exhaust or heat rejection is isohoric and isobaric

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What is the most efficient engine cycle?

Carnot

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What is the least efficient engine cycle?

Diesel

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Question

What is the net power  output of an engine if the frictional power is 15kW and the indicated power is 35kW?

20kW

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What is the net powet output of an engine if the torque of the crankshaft is 120Nm and the angular velocity is 50rad/s?

6kW

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What is the mechanical efficiency of an engine if the brake power if 50KW and the indicated power if 80kW?

0.625 or 62.5%

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What is the maximum input power of a an engine that consumes 500g/s and the calorific value of fuel is 44MJ/kg ?

22MW

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What is the indicated power if the overal efficiency is 70% , the input power is 20kW, and the mechanical efficiency is 40% ?

35kW

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Which of the following sentences is  true for an engine?

The indicating power is always greater than frictional or brake power.

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Are liquids and gases fluids?

Yes, they are.

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Which of the following is a key difference between fluids and gases?

Fluids are not compressible whereas gases are.

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What is a non-flow process?

A process in which there is no mass exchange.

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Question

Name two things that a non-flow process can share with its surroundings.

Heat and work.

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Name the three variables that can define a gas in a non-flow process.

Temperature, volume, and pressure.

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Question

What are the four non-flow processes?

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