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3.S: The First Law of Thermodynamics (Summary)

Key Terms

adiabatic process process during which no heat is transferred to or from the system
boundary imagined walls that separate the system and its surroundings
closed system system that is mechanically and thermally isolated from its environment
cyclic process process in which the state of the system at the end is same as the state at the beginning
environment outside of the system being studied
equation of state describes properties of matter under given physical conditions
equilibrium thermal balance established between two objects or parts within a system
extensive variable variable that is proportional to the amount of matter in the system
first law of thermodynamics the change in internal energy for any transition between two equilibrium states is \(ΔE_{int}=Q−W\)
intensive variable variable that is independent of the amount of matter in the system
internal energy average of the total mechanical energy of all the molecules or entities in the system
isobaric process process during which the system’s pressure does not change
isochoric process process during which the system’s volume does not change
isothermal process process during which the system’s temperature remains constant
molar heat capacity at constant pressure quantifies the ratio of the amount of heat added removed to the temperature while measuring at constant pressure
molar heat capacity at constant volume quantifies the ratio of the amount of heat added removed to the temperature while measuring at constant volume
open system system that can exchange energy and/or matter with its surroundings
quasi-static process evolution of a system that goes so slowly that the system involved is always in thermodynamic equilibrium
reversible process process that can be reverted to restore both the system and its environment back to their original states together
surroundings environment that interacts with an open system
thermodynamic process manner in which a state of a system can change from initial state to final state
thermodynamic system object and focus of thermodynamic study

Key Equations

Equation of state for a closed system \(f(p,V,T)=0\)
Net work for a finite change in volume \(W=∫^{V_2}_{V_1}pdV\)
Internal energy of a system (average total energy) \(E_{int}=\sum_i(\bar{K_i}+\bar{U_i})\),
Internal energy of a monatomic ideal gas \(E_{int}=nN_A(\frac{3}{2}k_BT)=\frac{3}{2}nRT\)
First law of thermodynamics \(ΔE_{int}=Q−W\)
Molar heat capacity at constant pressure \(C_p=C_V+R\)
Ratio of molar heat capacities \(γ=C_p/C_V\)
Condition for an ideal gas in a quasi-static adiabatic process \(pV^γ=constant\)


3.1 Thermodynamic Systems

  • A thermodynamic system, its boundary, and its surroundings must be defined with all the roles of the components fully explained before we can analyze a situation.
  • Thermal equilibrium is reached with two objects if a third object is in thermal equilibrium with the other two separately.
  • A general equation of state for a closed system has the form \(f(p,V,T)=0\), with an ideal gas as an illustrative example.

3.2 Work, Heat, and Internal Energy

  • Positive (negative) work is done by a thermodynamic system when it expands (contracts) under an external pressure.
  • Heat is the energy transferred between two objects (or two parts of a system) because of a temperature difference.
  • Internal energy of a thermodynamic system is its total mechanical energy.

3.3 First Law of Thermodynamics

  • The internal energy of a thermodynamic system is a function of state and thus is unique for every equilibrium state of the system.
  • The increase in the internal energy of the thermodynamic system is given by the heat added to the system less the work done by the system in any thermodynamics process.

3.4 Thermodynamic Processes

  • The thermal behavior of a system is described in terms of thermodynamic variables. For an ideal gas, these variables are pressure, volume, temperature, and number of molecules or moles of the gas.
  • For systems in thermodynamic equilibrium, the thermodynamic variables are related by an equation of state.
  • A heat reservoir is so large that when it exchanges heat with other systems, its temperature does not change.
  • A quasi-static process takes place so slowly that the system involved is always in thermodynamic equilibrium.
  • A reversible process is one that can be made to retrace its path and both the temperature and pressure are uniform throughout the system.
  • There are several types of thermodynamic processes, including (a) isothermal, where the system’s temperature is constant; (b) adiabatic, where no heat is exchanged by the system; (c) isobaric, where the system’s pressure is constant; and (d) isochoric, where the system’s volume is constant.
  • As a consequence of the first law of thermodymanics, here is a summary of the thermodymaic processes:
    • (a) isothermal: \(ΔE_{int}=0,Q=W\); 
    • (b) adiabatic: \(Q=0,ΔE_{int}=−W\) ; 
    • (c) isobaric: \(ΔE_{int}=Q−W\); and
    • (d) isochoric: \(W=0,ΔE_{int}=Q\).

3.5 Heat Capacities of an Ideal Gas

  • For an ideal gas, the molar capacity at constant pressure \(C_p\) is given by \(C_p=C_V+R=dR/2+R\), where d is the number of degrees of freedom of each molecule/entity in the system.
  • A real gas has a specific heat close to but a little bit higher than that of the corresponding ideal gas with \(C_p≃C_V+R\).

3.6 Adiabatic Processes for an Ideal Gas

  • A quasi-static adiabatic expansion of an ideal gas produces a steeper pV curve than that of the corresponding isotherm.
  • A realistic expansion can be adiabatic but rarely quasi-static.


Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).