# How Does Heat Depend On Temperature?

## Defining Heat and Temperature

Heat and temperature are related but distinct concepts. Heat refers to the transfer of thermal energy between objects or systems, while temperature measures the average kinetic energy of molecules and atoms. Heat is measured in joules (J) or calories (cal), quantifying the total thermal energy. Temperature is measured in kelvin (K), Celsius (°C), or Fahrenheit (°F), indicating the average molecular kinetic energy which relates to the “hotness” or “coldness” felt during touch.

While heating increases temperature, the total heat depends on the mass, specific heat capacity, and temperature change. Heating the same mass of different materials by the same amount can result in different temperature rises, due to differences in molecular heat capacity. Temperature measures the average energy per molecule, while heat measures the total thermal energy transfer.

## Heat is Energy Flow, Temperature Measures Average Kinetic Energy

Heat is a form of energy that is transferred between objects or systems due to their temperature difference. When two objects at different temperatures come into thermal contact, heat flows from the hotter object to the colder one until they reach thermal equilibrium. This heat transfer occurs at the microscopic level as the more energetic particles in the hotter object collide with the less energetic particles in the colder object, transferring kinetic energy between them.

Temperature is a measure of the average kinetic energy of microscopic particles that make up a substance. As an object gets hotter, its molecules and atoms vibrate and move faster, gaining kinetic energy. Temperature is the macroscopic manifestation of this microscopic kinetic energy. Objects with a higher temperature have particles moving faster on average than objects with a lower temperature.

While heat and temperature are related, they are distinct physical quantities. Heat is energy transferred due to a temperature difference, while temperature measures the average kinetic energy of particles. An object can gain heat without its temperature changing if its heat capacity is high enough. Understanding the link between microscopic kinetic energy, temperature, and heat transfer is key to explaining many thermodynamic processes.

## Heat Flow Increases with Temperature Difference

The rate of heat transfer between two objects depends on the temperature difference between them. The greater the temperature difference, the faster heat will flow from the hotter object to the colder one. This is because heat always moves spontaneously from higher temperature to lower temperature.

For example, if you touch an object at 100°C with your hand at 37°C, heat will flow rapidly from the hot object into your cooler hand. However, if you touch an object at 40°C, the heat flow will be slower because the temperature difference is less.

This relationship can be quantified through the heat transfer rate equation:

Q/t = kA(ΔT)

Where Q is the heat transfer, t is time, k is the thermal conductivity, A is the surface area, and ΔT is the temperature difference. This shows mathematically that the rate of heat flow (Q/t) is directly proportional to the temperature difference.

In summary, the driving force for heat transfer is the temperature gradient. The steeper the temperature gradient, the faster heat will flow between objects until they reach thermal equilibrium.

## Heat Capacity Relates Heat and Temperature Change

An object’s heat capacity is a measure of the amount of heat energy required to raise its temperature. Heat capacity depends on the mass, state, and composition of the material.

Materials with high heat capacity require more heat to increase their temperature. This is because they can store more thermal energy per degree of temperature change. For example, water has a very high heat capacity, which is why bodies of water heat and cool slowly compared to land. Metals like iron and lead also have high heat capacities.

Materials with low heat capacity, like air, require less heat to increase their temperature. A given amount of heat energy causes a larger temperature change in materials with low heat capacity.

Therefore, heat capacity relates the amount of heat added or removed to the resulting temperature change. High heat capacity materials experience smaller temperature changes for the same heat transfer. Low heat capacity materials undergo larger temperature changes for the same amount of heat added or removed.

## Phase Changes Impact Heat Capacity

When a substance undergoes a phase change, such as melting, boiling, freezing, or condensing, its temperature remains constant even as heat is added or removed. This is because the heat is providing the energy required to break down the molecular bonds during these transitions between solid, liquid, and gas phases. The heat absorbed during a phase change does not cause a temperature rise but allows the phase change to occur.

The amount of heat energy required to change the phase of a unit mass of a substance is called latent heat. For example, the latent heat of fusion is the energy needed to melt a solid to a liquid, while the latent heat of vaporization is the energy needed to boil a liquid into a gas. Substances have very high heat capacities during phase changes as they absorb or release large amounts of latent heat at constant temperature.

Understanding the latent heats of phase changes for water and other materials is very useful for designing systems that utilize phase changes like HVAC, power generation, chemical processing, and more. The high heat capacity of water makes it exceptionally good at temperature regulation. For example, the high latent heat of vaporization of water allows sweat to efficiently cool the human body.

## Conduction Heat Transfer

Conduction is the transfer of heat between two objects in direct physical contact. It occurs when faster moving hot molecules collide with slower moving cold molecules, transferring kinetic energy. Metals like copper and aluminum are good conductors of heat because they contain many free electrons that can transport thermal energy rapidly through the metal. Insulators like glass and plastic have far fewer free electrons, so they resist the conduction of heat. This is why insulated cups keep drinks hot or cold longer.

The rate of conductive heat transfer depends on the temperature difference, the conductive properties of the material, and the contact area. Larger temperature differences, more conductive materials, and greater contact areas lead to faster heat conduction. This is why metal feels colder than wood, for example. The higher conductivity of the metal rapidly draws heat away from your hand.

## Convection Heat Transfer

Convection is the mode of heat transfer through the bulk movement of fluids. Convection can transport thermal energy rapidly compared to conduction because the energy is carried by the overall motion of the fluid. There are two main types of convection – natural convection and forced convection.

In natural convection, fluid motion occurs due to differences in density created by temperature variations in the fluid. For example, when water is heated in a pot, the warmer water near the bottom of the pot expands, becomes less dense, and rises while the cooler water sinks to take its place – creating circulation. Natural convection also causes wind and ocean currents on a global scale due to temperature differences.

Forced convection occurs when an external source causes the fluid motion, such as a fan blowing air or a pump circulating water. Forced convection can greatly increase the rate of heat transfer beyond what natural convection would achieve. Examples include forced air furnaces and water cooling systems in engines/computers. The fluid velocity determines the convection heat transfer rate.

Radiation heat transfer involves the transfer of heat via electromagnetic waves or photons. This does not require a medium like a solid, liquid or gas and allows heat to be transferred through a vacuum. All objects with a temperature above absolute zero emit thermal radiation. This radiation gets transmitted through space at the speed of light until it hits and gets absorbed by another object. The rate of radiative heat transfer depends on the emissivity of the surface emitting the radiation as well as the absorptivity of the surface receiving the radiation. Reflective and polished surfaces have low emissivities while rough and black surfaces have high emissivity, allowing them to efficiently absorb and emit thermal radiation. Radiation allows the sun’s energy to travel through the vacuum of space and heat objects on Earth. It also allows heat transfer to occur between objects that aren’t in direct contact, like between the Earth and the upper atmosphere.

## Real-World Applications

The principles of heat and temperature are critical in many real-world applications. For example, heating and cooling systems rely on the flow of heat to regulate indoor temperatures. Furnaces and air conditioners use convection to circulate hot and cold air. Insulation materials like fiberglass batts or rigid foam boards are used to limit heat conduction through walls, attics, and basements. This helps reduce energy costs for heating and cooling homes and buildings.

Cooking also depends heavily on heat transfer. The heating elements or burners in stoves and ovens convert electricity or gas into thermal energy which is then transferred to the food via conduction and convection. Radiation from the heating elements also warms the food. Insulated handles and knobs prevent excess heat conduction to the exterior of appliances.

Internal combustion engines in cars and machinery rely on heat transfer too. Fuel is burned to convert chemical energy into heat which raises the temperature and pressure inside the cylinders. This thermal energy expands the gases and moves the pistons in the engine. Engine cooling systems transfer excess heat away using liquid coolants and radiators.

In all these examples, understanding the relationship between heat and temperature is key to designing effective systems and processes. Controlling heat flow by limiting temperature differences and using insulators or conductors is critical across many realms of science and engineering.

## Summary

In summary, while heat and temperature are related concepts, they have distinct definitions. Heat refers to the transfer of thermal energy between objects or systems, while temperature measures the average kinetic energy of molecules. As temperature difference increases between objects or systems, the potential rate of heat transfer also increases, according to the laws of thermodynamics. Materials have different heat capacities, which describe how much heat is needed to change their temperature. There are also different mechanisms for heat transfer like conduction, convection, and radiation. Understanding the relationship between heat and temperature, along with the heat capacities and transfer mechanisms of different materials, allows us to engineer solutions for managing heat flow in real-world applications.