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Heat Engines

Heat Engines

A heat engine is a device used to extract heat from a source and then convert it into mechanical work used for various applications. For example, a steam engine on an old-style train can produce the work needed for driving the train.
Whenever we consider heat engines (and associated devices such as refrigerators and heat pumps), we do not use the standard sign convention for heat and work. For convenience, we assume that the symbols Qh, Qc, and W represent only the amounts of heat transferred...

Mechanisms of Heat Transfer I

Mechanisms of Heat Transfer I

Just as interesting as the effects of heat transfer on a system are the methods by which the heat transfer occur. Whenever there is a temperature difference, heat transfer occurs. It may occur rapidly, such as through a cooking pan, or slowly, such as through the walls of a picnic ice box. So many processes involve heat transfer that it is hard to imagine a situation where no heat transfer occurs. Yet, every heat transfer takes place by only three methods: conduction, convection, and radiation.

Mechanisms of Heat Transfer II

Mechanisms of Heat Transfer II

In convection, thermal energy is carried by the large-scale flow of matter. Ocean currents and large-scale atmospheric circulation, which result from the buoyancy of warm air and water, transfer hot air from the tropics toward the poles and cold air from the poles toward the tropics. The Earth’s rotation interacts with those flows, causing the observed eastward flow of air in the temperate zones. Convection dominates heat transfer by air, and the amount of available space for the airflow...

Mechanisms of Heat Transfer

Mechanisms of Heat Transfer

Heat transfer between the human body and its environment occurs through four main mechanisms: conduction, convection, radiation, and evaporation.
Conduction, accounting for approximately 3% of body heat loss at rest, is the process of exchanging heat between molecules of two materials in direct contact. This can result in both heat loss and gain. For instance, when the body is submerged in water, which conducts heat 20 times more effectively than air, it can either lose or gain significant heat.

Maxwell-Boltzmann Distribution: Problem Solving

Maxwell-Boltzmann Distribution: Problem Solving

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by

Entropy

Entropy

The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...

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Updated: Jun 20, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Stochastic heat engine using a single Brownian ellipsoid.

Soham Dutta¹, Arnab Saha^1,2

¹University of Calcutta, Department of Physics, 92, Acharya Prafulla Chandra Road, Kolkata 700009, India.

Physical Review. E

|June 19, 2026

Summary

This summary is machine-generated.

We developed a microscopic Stirling engine model using a Brownian ellipsoid. This engine converts heat into work, with performance depending on ellipsoid geometry and orientation, offering insights into nanoscale thermodynamics.

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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

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Published on: August 12, 2013

Area of Science:

Thermodynamics
Statistical Mechanics
Nanotechnology

Background:

Optical tweezers enable precise manipulation of microscopic particles.
Brownian motion describes the random movement of particles suspended in a fluid.
Stirling engines are heat engines operating via a closed regenerative thermodynamic cycle.

Purpose of the Study:

To propose a theoretical model of a microscopic Stirling engine.
To utilize a Brownian ellipsoid as the working substance.
To analyze the engine's performance based on particle geometry and orientation.

Main Methods:

Developing a theoretical model for a microscopic Stirling engine.
Using optical tweezers to confine a Brownian ellipsoid harmonically.
Coupling the ellipsoid's degrees of freedom to thermal baths with time-periodic stiffness.
Analyzing operational characteristics in the quasistatic regime.

Main Results:

The engine converts heat from a hot bath into thermodynamic work.
Extracted work and input heat depend on the ellipsoid's geometry and orientation.
Dissipative coupling influences engine optimization.
Analytical results in the slightly anisotropic regime agree well with numerical simulations.

Conclusions:

A novel microscopic Stirling engine model using a Brownian ellipsoid was proposed.
The engine's efficiency and work output are tunable via particle anisotropy.
This work provides a framework for understanding nanoscale heat engines and their optimization.