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

- Page ID
- 10272

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## 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 | \(pV^γ=constant\) |

### Summary

### 3.2 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.

### 3.3 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.

### 3.4 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.

### 3.5 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: \(W=0,ΔE_{int}=Q\).

### 3.6 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 \(C_p≃C_V+R\).

### 3.7 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.

## Contributors and Attributions

Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).