Thermodynamics

SYNOPSIS

• Thermodynamics deals with the exchange of heat between a body and the surrounding along with other processes accompanying it.
• The nature of heat and its relationship to mechanical work was studied by Joule.
• Thermal equilibrium implies that systems are at the same temperature.
• Internal energy of a system is the sum of kinetic energies and potential energies of the molecular constituents of the system. It does not include the overall kinetic energy of the system.
• Equilibrium states of a thermodynamic system are described by state variables. The value of a state variable depends only on the particular state and not on the path used to arrive at that state.
• Examples of state variables are pressure (P), volume (V), temperature (T) and mass (m). Heat and work are not state variables.
• Zeroth law of thermodynamics: Two systems in thermal equilibrium with a third system are in thermal equilibrium with each other.
• The first law of thermodynamics is based on the principle of conservation of energy.
  ∆U = ∆Q − P∆V
• Efficiency of a heat engine is the ratio of work done by the engine to input heat.
  
  
• If all the input heat is converted entirely to heat, then the engine would have an efficiency of 1.
• In a reversible process, both the system and its environment can be returned to their initial states.
• Spontaneous processes of nature are irreversible. The idealised reversible process is a quasi-static process with no dissipative factors such as friction, viscosity etc.
• A quasi-static process is an infinitely slow process such that the system remains in thermal and mechanical equilibrium with the surroundings throughout. In a quasi-static process, the pressure and temperature of the environment can differ from those of the system only infinitesimally.
• A heat engine is a device in which a system undergoes a cyclic process resulting in conversion of heat to work.
• The Carnot engine is a reversible engine operating between two temperatures T1 (source) and T2 (sink). The Carnot cycle consists of two isothermal processes connected by two adiabatic processes.
  
  
• The efficiency of the Carnot engine is independent of the working substance of the engine. It only depends on the temperatures of the hot and cold reservoirs.
• Efficiency of the Carnot engine is 𝜂 = 1 − T_C/T_H = 1 − (Temperature of cold reservoir/Temperature of hot reservoir).
• The efficiency of an engine is never more than that of a Carnot engine.
1. Heat lost by a hot body = heat gained by a cold body
2. Heat can flow from cooler surroundings into a hotter body (e.g. coffee) to make it hotter.
• Kelvin’s statement of the second law of thermodynamics:
  No heat engine can convert heat to work with 100% efficiency.
• Clausius statement: No process is possible whose sole result is the transfer of heat from a colder body to a hotter body.
• Kelvin’s statement: No process is possible whose sole result is the complete conversion of heat to work.
• Coefficient of performance of a refrigerator is α = Q_C/W.
• A heat pump is called so because it pumps heat from the cold outdoors (cold reservoir) into the warm house (hot reservoir).
• When Q > 0, heat is added to the system.
  When Q < 0, heat is removed from the system.
  When W > 0, work is done by the system.
  When W < 0, work is done on the system.
•  Heat engine
  
  
• Work done by a heat engine