Thermodynamics: Heat, Temperature and Energy
Thermodynamics is the branch of physics that studies heat, temperature, work and internal energy, and the transformations between them. It rests on a few laws that govern every engine, refrigerator and power plant in the world. For candidates preparing for the APSC, Assam Direct Recruitment, SSC and other competitive examinations of Assam, thermodynamics is extremely important because it combines conceptual questions on the laws of thermodynamics with numerical problems on specific heat, latent heat, thermal expansion and the efficiency of heat engines. A firm grasp of these ideas, together with correct SI units, is essential for scoring well.
Basic Terms
- Heat (Q): Energy transferred between bodies because of a temperature difference. Its SI unit is the joule (J); the calorie is 4.18 J.
- Temperature: A measure of the average kinetic energy of the molecules of a body. Its SI unit is the kelvin (K).
- Internal energy (U): The sum of all kinetic and potential energies of the molecules of a system. It is a state function.
- Specific heat capacity (c): The heat required to raise the temperature of unit mass by one kelvin. For water it is about 4186 J per kilogram per kelvin.
- Latent heat (L): The heat required to change the state of unit mass at constant temperature; for water, the latent heat of fusion is about 3.34 x 10^5 J/kg and of vaporisation about 2.26 x 10^6 J/kg.
- Thermal expansion: The increase in the dimensions of a body on heating, described by linear, areal and volume coefficients.
- Entropy (S): A measure of the disorder or randomness of a system; its SI unit is joule per kelvin.
- Heat engine: A device that converts heat into work and has an efficiency less than one.
Core Concepts and Formulas
- Heat gained or lost: Q = m c delta-T, where delta-T is the change in temperature.
- Latent heat: Q = m L at constant temperature.
- Linear expansion: delta-L = L alpha delta-T; areal expansion: delta-A = A beta delta-T; volume expansion: delta-V = V gamma delta-T, with gamma = 3 alpha.
- First law of thermodynamics: delta-U = Q minus W, where W is the work done by the system.
- Work by a gas at constant pressure: W = P delta-V.
- Ideal gas equation: P V = n R T, with R = 8.314 joule per mole per kelvin.
- Efficiency of a heat engine: eta = 1 minus (Q-two by Q-one) or eta = W by Q-one.
- Carnot efficiency: eta = 1 minus (T-two by T-one), the temperatures being in kelvin.
- Coefficient of performance of a refrigerator: beta = Q-two by W.
- Second law: heat cannot flow spontaneously from a colder body to a hotter body, and entropy of an isolated system never decreases.
- Change in entropy: delta-S = Q by T for a reversible process.
The Nature of Heat and Temperature
Heat and temperature are related but different quantities. Temperature tells how hot or cold a body is, while heat is the energy that flows from a hotter body to a colder one because of the temperature difference. When two bodies at different temperatures are placed in contact, heat flows until thermal equilibrium is reached, at which point they have the same temperature. This is the zeroth law of thermodynamics, and it makes the measurement of temperature possible. The Celsius, Fahrenheit and Kelvin scales are related by simple conversion formulas, and all thermodynamic formulas must use the absolute, or Kelvin, scale.
The Laws of Thermodynamics
The first law of thermodynamics is the law of conservation of energy applied to heat processes: the heat supplied to a system equals the increase in its internal energy plus the work done by the system, so delta-U = Q minus W. The second law imposes the direction of natural processes: heat flows spontaneously from hot to cold, and no engine can convert all the absorbed heat into work. The third law states that the entropy of a perfectly ordered crystal approaches zero as the temperature approaches absolute zero. Together, these laws set the limits on all energy conversions.
Specific Heat and Calorimetry
Calorimetry is the measurement of heat exchange. The principle of calorimetry states that in an isolated system, the heat lost by the hot body equals the heat gained by the cold body. Using Q = m c delta-T for each body and equating the magnitudes, we can find the unknown specific heat or the final temperature. Water has a very high specific heat capacity of about 4186 J per kilogram per kelvin, which is why it is used as a coolant and why coastal regions have a moderate climate. This concept also explains why Sandy and clay soils heat up faster than water during the day.
Latent Heat and Change of State
During a change of state, the temperature of a substance remains constant even though heat is being supplied, because the energy is used to overcome intermolecular forces rather than to raise the temperature. The heat absorbed at constant temperature by unit mass is the latent heat. The latent heat of fusion of ice is about 3.34 x 10^5 J/kg and the latent heat of vaporisation of water is about 2.26 x 10^6 J/kg. This explains why steam at 100 degrees Celsius causes more severe burns than water at the same temperature: steam releases a large amount of latent heat when it condenses.
Thermal Expansion
Most solids and liquids expand when heated because the average separation between molecules increases. The fractional change in length, area or volume per kelvin is called the coefficient of linear, areal or volume expansion. For an isotropic solid, the coefficient of volume expansion is three times the coefficient of linear expansion. Applications include the deliberate gaps left in railway tracks and bridges, the bimetallic strip used in thermostats, and the fitting of metal rims onto wooden wheels. Water is anomalous: it contracts from 0 to 4 degrees Celsius and expands above 4 degrees Celsius, which is crucial for the survival of aquatic life in cold winters.
Heat Transfer: Conduction, Convection and Radiation
Heat is transferred in three ways. Conduction occurs mainly in solids through the vibration of molecules without the movement of the material itself, and is described by the rate of flow proportional to the area times the temperature gradient. Convection occurs in fluids through the actual movement of heated portions, as in boiling water and land breezes. Radiation is the transfer of heat by electromagnetic waves and requires no medium, which is how the Sun's heat reaches the Earth. Newton's law of cooling states that the rate of cooling of a body is proportional to the excess of its temperature over its surroundings. A black body is the best absorber and emitter of radiation.
Entropy and the Second Law
Entropy is a measure of the disorder of a system. The second law of thermodynamics states that the total entropy of an isolated system never decreases; naturally occurring processes move towards greater disorder. For example, heat flows from hot to cold, gases expand to fill their container, and ink diffuses through water, all because these processes increase entropy. The concept of entropy explains why perpetual motion machines of the second kind are impossible and provides the theoretical limits on the efficiency of engines and refrigerators.
Heat Engines and Refrigerators
A heat engine takes heat Q-one from a hot reservoir, converts part of it into work W and rejects the rest Q-two to a cold reservoir. Its efficiency is the ratio of the work done to the heat absorbed, and it is always less than one. The Carnot engine is an ideal reversible engine that gives the maximum possible efficiency between two temperatures, eta = 1 minus T-two by T-one. Real engines, such as the petrol and diesel engines and the steam turbine, have efficiencies reduced by friction and other irreversible losses. A refrigerator is a heat engine run in reverse: it extracts heat from a cold region by doing work on the working substance.
Solving Numerical Problems
In numerical problems, first identify whether the question involves temperature change or a change of state. If the temperature changes, use Q = m c delta-T; if a state changes, use Q = m L; and if both occur, handle each stage separately. For gas problems, use P V = n R T and the first law. Convert all temperatures to kelvin before using the gas law or the Carnot formula. For engine efficiency, find the work as Q-one minus Q-two and divide by Q-one. Careful bookkeeping of units, and checking that efficiency is less than one hundred per cent, will prevent most errors.
Applications of Thermodynamics
Thermodynamics underlies the working of steam turbines in power generation, internal combustion engines in vehicles, refrigerators and air conditioners, and heat pumps. It is central to understanding weather and climate, the melting of glaciers, and the performance of solar thermal systems. In daily life in Assam, it explains why tea cools faster when pored into a saucer, why pressure cookers cook food quickly, and why we wear woollen clothes in winter.
Common Mistakes to Avoid
- Using degrees Celsius where kelvin is required, especially in the Carnot and gas-law formulas.
- Confusing heat with temperature; heat is energy in transit, while temperature measures molecular kinetic energy.
- Adding sensible heat and latent heat in a single step without treating the change of state separately.
- Writing the first law with the wrong sign for the work done by or on the system.
- Forgetting that efficiency must be less than one hundred per cent, and that the Carnot value is only a theoretical maximum.
- Assuming that all substances expand on heating; noting the anomalous expansion of water.
- Mixing up the three coefficients of thermal expansion and the relation gamma equal to three alpha.
How to Prepare This Topic
- Learn the definitions and SI units of heat, temperature, internal energy, specific heat, latent heat and entropy.
- Memorise the key formulas and practise converting between Celsius, Fahrenheit and Kelvin.
- Solve a large number of calorimetry and change-of-state problems step by step.
- Draw labelled diagrams of the Carnot cycle and pipe flow in a steam engine to visualise the processes.
- Attempt previous-year question papers and revise the laws and their statements regularly.
Frequently Asked Questions
What is the first law of thermodynamics?
It is the law of conservation of energy for heat processes: the heat supplied to a system equals the increase in its internal energy plus the work done by the system, delta-U = Q minus W.
Why does the temperature remain constant during a change of state?
Because the heat supplied is used to overcome the intermolecular forces and change the state, not to raise the average kinetic energy, so the temperature does not change until the change of state is complete.
Why is the specific heat capacity of water so high?
Water has a specific heat capacity of about 4186 J per kilogram per kelvin because of strong hydrogen bonding, so it can absorb a lot of heat with a small temperature rise, making it a good coolant.
What is the efficiency of a Carnot engine?
It is the maximum possible efficiency between two reservoirs, given by eta = 1 minus T-two by T-one, where the temperatures are in kelvin. It is always less than one hundred per cent unless the cold reservoir is at absolute zero.
What does the second law of thermodynamics state?
It states that heat cannot flow spontaneously from a colder body to a hotter body, and that the entropy of an isolated system never decreases. It fixes the direction of natural processes and limits engine efficiency.