a branch of physics that studies the exchange and transformation of energy in macroscopic systems, especially in the form of heat and work
Formula for the internal energy of an ideal monatomic gas: U = (3/2)·n·R·T = (3/2)·p·V — depends on amount of substance, temperature, pressure, and volume
Internal energy is the kinetic energy of all particles within the system. The formulas are applicable to an ideal monatomic gas. For a more general case, U = (i/2)·n·R·T is used, where i is the number of degrees of freedom.
Formula for change in internal energy: ΔU = (3/2)·(m/μ)·R·ΔT for a monatomic gas or ΔU = (i/2)·(m/μ)·R·ΔT for any ideal gas with i degrees of freedom
The formula gives the change in internal energy during heating or cooling. The first expression is for a monatomic gas, the second is a universal form. ΔT — change in temperature; i — number of degrees of freedom of the substance.
Formula for gas work during volume change: A = p·ΔV — product of pressure and change in volume
Work is positive if the system expands (ΔV > 0). This expression is valid at constant pressure.
First law of thermodynamics: Q = ΔU + A — the amount of heat transferred to the system goes into changing its internal energy and performing work
The heat Q received by the system goes into changing its internal energy ΔU
and performing work A against external forces.
If Q > 0 — heat enters the system; Q < 0 — the system loses heat.
A > 0 — the system expands and performs work; A < 0 — the system compresses.
Formula for quantity of heat: Q = c·m·ΔT or Q = C·n·ΔT — depends on mass or amount of substance, heat capacity, and temperature change
The formulas are used to calculate heat during substance heating: c — specific heat capacity, m — mass, C — molar heat capacity, n — amount of substance. ΔT — temperature difference (final minus initial).
Formula for thermal machine efficiency: η = A / Q₁ = (Q₁ - Q₂) / Q₁ = 1 - Q₂ / Q₁ — shows what fraction of received heat is converted into useful work
Efficiency is the fraction of received heat converted into useful work. Q₁ — amount of heat received from the hot reservoir; Q₂ — amount of heat given to the cold reservoir. The smaller Q₂, the higher the machine's efficiency.
Formula for Carnot cycle efficiency: η = (T₁ - T₂) / T₁ = 1 - T₂ / T₁ — maximum theoretical efficiency of a heat engine operating between two temperatures
The Carnot cycle is an ideal reversible process consisting of two isothermal and two adiabatic stages. Its efficiency depends only on the temperatures of the hot reservoir (T₁) and cold reservoir (T₂), and not on the nature of the working substance. The formula shows the maximum theoretical efficiency achievable at given temperatures.
Formula for quantity of heat during melting or freezing: Q = λ·m — product of specific latent heat of fusion and mass of substance
λ — specific latent heat of fusion (or crystallization); m — mass of substance. The formula gives the amount of heat required for a transition between solid and liquid states at constant temperature.
Formula for quantity of heat during vaporization or condensation: Q = r·m — product of specific latent heat of vaporization (or condensation) and mass of substance
r — specific latent heat of vaporization (or condensation); m — mass of substance. Heat is not used for heating, but for changing the state of aggregation — from liquid to gas or vice versa.