Physics > Thermodynamics

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  • Zeroth Law of Thermodynamics states that 'two systems in thermal equilibrium with a third system separately are in thermal equilibrium with each other'.
  • The Zeroth Law clearly suggests that when two systems  and , are in thermal equilibrium, there must be a physical quantity that has the same value for both. This thermodynamic variable whose value is equal for two systems in thermal equilibrium is called 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 over-all kinetic energy of the system. Heat and work are two modes of energy transfer to the system. Heat is the energy transfer arising due to temperature difference between the system and the surroundings. Work is energy transfer brought about by other means, such as moving the piston of a cylinder containing the gas, by raising or lowering some weight connected to it.
  • The first law of thermodynamics is the general law of conservation of energy applied to any system in which energy transfer from or to the surroundings (through heat and work) is taken into account. It states that

    where is the heat supplied to the system,  is the work done by the system and  is the change in internal energy of the system.

  • The specific heat capacity of a substance is defined by

    where  is the mass of the substance and  is the heat required to change its temperature by

    The molar specific heat capacity of a substance is defined by

    where μ is the number of moles of the substance. For a solid, the law of equipartition of energy gives

    which generally agrees with experiment at ordinary temperatures.

    For an ideal gas, the molar specific heat capacities at constant pressure and volume satisfy the relation

    where R is the universal gas constant.

  • Equilibrium states of a thermodynamic system are described by state variables. The value of a state variable depends only on the particular state, not on the path used to arrive at that state. Examples of state variables are pressure , volume , temperature , and mass  Heat and work are not state variables. An Equation of State (like the ideal gas equation  is a relation connecting different state variables.
  • 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.
  •  In an isothermal expansion of an ideal gas from volume  to at temperature T the heat absorbed  equals the work done  by the gas, each given by

  • In an adiabatic process of an ideal gas

  • Heat engine is a device in which a system undergoes a cyclic process resulting in conversion of heat into work. If  is the heat absorbed from the source,  is the heat released to the sink, and the work output in one cycle is , the efficiency η of the engine is:

  • In a refrigerator or a heat pump, the system extracts heat  from the cold reservoir and releases  amount of heat to the hot reservoir, with work  done on the system. The co-efficient of performance of a refrigerator is given by
  • The second law of thermodynamics disallows some processes consistent with the First Law of Thermodynamics.

     No process is possible whose sole result is the absorption of heat from a reservoir and complete conversion of the  heat into work.

Clausius statement

No process is possible whose sole result is the transfer of heat from a colder object to a hotter object.

Put simply, the Second Law implies that no heat engine can have efficiency  equal to 1 or no refrigerator can have co-efficient of performance α equal to infinity.

A process is reversible if it can be reversed such that both the system and the surroundings return to their original states, with no other change anywhere else in the universe.

Spontaneous processes of nature are irreversible. The idealised reversible process is a quasi-static process with no dissipative factors such as friction, viscosity, etc.

  • Carnot engine is a reversible engine operating between two temperatures  (source) and  (sink). The Carnot cycle consists of two isothermal processes connected by two adiabatic processes. The efficiency of a Carnot engine is given by

    No engine operating between two temperatures can have efficiency greater than that of the Carnot engine.

    If , heat is added to the system

    If  heat is removed to the system

    If  Work is done by the system

    If  Work is done on the system

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