# How Heat Work And Energy Are Closely Related?

## Definition of Heat

Heat is the transfer of thermal energy between objects due to a temperature difference. When two objects with different temperatures come in contact, heat will spontaneously flow from the hotter object to the colder one until they reach thermal equilibrium. The amount of heat transferred depends on the temperature difference, the materials involved, and how well they conduct heat.

On a microscopic level, heat arises from the random motions of atoms and molecules. In hotter objects, the particles have more kinetic energy and vibrate faster. Transferring some of this energy to a colder object increases the motion of its particles, raising its temperature. Heat always moves spontaneously from hot to cold in order to distribute energy more uniformly.

While related, heat and temperature are distinct. Temperature measures the average internal kinetic energy of an object’s atoms, while heat refers to the transfer of thermal energy between objects at different temperatures. Understanding this distinction is key to describing heat flow and energy transfer.

## Definition of Work

In physics, work is defined as a force exerted on an object that causes the object to be displaced or move in the direction of the applied force. Work is only done on an object when the force applied causes the object to move. If the object does not move, no work is performed regardless of how much force is exerted.

Mathematically, work can be calculated as the product of the force (F) applied on an object and the displacement (d) of the object in the direction of the force:

Work = Force x Displacement

W = Fd

The unit of work is the joule (J) which is equal to a newton-meter (Nm) or kg∙m2/s2. The amount of work done on an object depends on two key factors – how much force is exerted and over what distance or displacement. The greater the force and displacement, the more work is done.

## Relationship Between Heat and Temperature

Heat and temperature are intrinsically linked. When heat is transferred to an object, the temperature of that object increases. This occurs because heat is a form of energy and temperature is a measure of the average kinetic energy of molecules within a substance. When heat is added, it increases the motion and vibrations of the molecules, thereby increasing the overall energy and temperature.

The amount of temperature increase depends on the heat capacity of the substance. Substances with a high heat capacity require more heat to increase the temperature. Substances with a low heat capacity heat up faster with the same heat input. But in all cases, adding heat increases molecular motion which manifests as a temperature rise.

This relationship is quantified in the heat capacity equations. For example, Q=mcΔT relates the amount of heat (Q), mass (m), specific heat capacity (c) and temperature change (ΔT). So the greater the heat input, the larger the resulting temperature change, illustrating their direct relationship.

## Relationship Between Work and Energy

Work and energy are closely related concepts in physics. Work involves applying a force to move an object, while energy is the capacity to do work. When work is done on an object, energy is transferred to or from that object.

For example, when you lift a book from the floor up onto a table, you are doing work on the book by applying an upward force over a distance. This work transfers energy to the book in the form of gravitational potential energy. The book gains potential energy equal to the work done on it.

In general, the work done on an object is equal to the change in the object’s energy. If positive work is done, the object gains energy. If negative work is done by opposing forces, such as friction, the object loses energy. Work and energy are directly proportional:

Work = Change in Energy

Or mathematically:

W = ΔE

Where W is work and ΔE is the change in energy. This relationship is one of the most important in physics and helps explain how energy transfers whenever work is done.

## First Law of Thermodynamics

The first law of thermodynamics is a fundamental physical law describing the relationship between heat and work. It states that the change in internal energy of a system is equal to the amount of heat supplied to the system minus the amount of work done by the system on its surroundings.

What this means is that energy can be transformed between heat and work while the total energy of a closed system remains constant. For example, an internal combustion engine converts the chemical energy contained in gasoline into mechanical work. The gasoline undergoes combustion, releasing heat. Some of this heat is then converted into useful mechanical work that turns the crankshaft. Meanwhile, some waste heat exits via the exhaust system.

The first law of thermodynamics is essentially a statement of the conservation of energy. The total energy of the universe remains constant – it is merely transformed between different forms. This law describes how heat and work are two ways of transferring energy in and out of a system, causing its internal energy to change accordingly while obeying the overall conservation of energy.

## Heat Engines

Heat engines are devices that convert heat into mechanical work. They operate on the basis of thermodynamic cycles, where a working fluid undergoes changes in temperature, pressure, and volume as it absorbs and rejects heat. The most common heat engines are internal combustion engines, steam turbines, and gas turbines.

In an internal combustion engine, fuel and air are burned inside a cylinder. This combustion process adds heat to the gases, causing them to rapidly expand. The expanding gases push a piston, producing usable mechanical work. The hot exhaust gases are then discharged.

Steam turbines also follow a cycle where water is boiled to high-pressure steam, which then expands across turbine blades, spinning them to do work. The used steam is condensed back into water and the cycle repeats. Gas turbines work similarly, except combusting fuel heats up and expands a gas like air instead of water vapor.

A key consideration for heat engines is their thermal efficiency. This is the fraction of heat input that gets converted into usable work, rather than being lost to the environment. Maximizing thermal efficiency is an ongoing area of research and design optimization for heat engines.

## Everyday Examples

Heat and work are intimately related in many everyday devices that supply power to our modern world:

• In car engines, the exploding fuel inside each cylinder generates heat which expands the gas, doing work to move the piston.

• In steam turbines at power plants, heat from burning coal boils water to produce high-pressure steam that pushes against the turbine blades to rotate a generator.

• In nuclear power plants, the nuclear fission reaction generates tremendous heat which is used to boil water, with the resulting steam driving turbines.

In all of these examples, heat is converted into mechanical work that can then be harnessed for useful purposes. The relationship between heat and work is fundamental to extracting power from chemical and nuclear reactions.

## Quantifying Heat and Work

Heat and work can be quantified and related mathematically using the following key equations:

The amount of heat (Q) is related to the change in temperature (ΔT), specific heat capacity (c), and mass (m) by:

Q = mcΔT

This shows that heat depends on how much the temperature changes during a process and the characteristics of the material.

Work (W) is related to pressure (P), change in volume (ΔV), and angle (for rotational mechanics) by:

W = PΔV

W = τθ

This demonstrates that work depends on the forces exerted and the resulting displacement or change in volume and angle.

The first law of thermodynamics relates heat, work, and internal energy (U) as:

ΔU = Q – W

This states that the change in a system’s internal energy is equal to the net heat added to the system minus the net work done by the system. This allows calculations relating heat, work, and internal energy for processes and cycles.

## Conservation of Energy

One of the most fundamental laws in physics is the law of conservation of energy. This law states that the total energy in an isolated system remains constant. Energy cannot be created or destroyed, but only transformed from one form into another.

This law applies directly to heat and work. When heat flows into a system, it adds energy to the system. When work is done by a system, it gives up some of its internal energy. However, the total amount of energy within the isolated system remains the same. The energy lost in the form of work is compensated by the energy gained in the form of heat.

For example, in a steam engine, the heat energy from burning fuel is transferred into mechanical work. The engine loses heat energy but gains work energy, however the total energy remains unchanged. The conservation of energy is upheld. This important physical law limits what is possible in heat engines and other thermodynamic processes.

## Summary

In summary, heat and work are closely related through the laws of thermodynamics. The First Law of Thermodynamics states that the internal energy of a closed system changes through heat and work. When heat is added to a system, it gains internal energy. When a system does work, it loses internal energy.

Work and energy are directly proportional. The energy transferred by mechanical work is equal to the force multiplied by the distance. Heat engines provide a clear example of the relationship between heat, work and energy. They convert thermal energy from a high temperature reservoir into mechanical work. The output work is always less than the input heat due to entropy and losses.

Everyday examples like vehicle engines, electric generators and metabolic processes in biology showcase this relationship between heat and work. By quantifying heat transfer and work done, we can apply conservation of energy to any process. The key takeaway is that heat and work are transfer mechanisms that change the internal energy of a system.