Isobaric process

In <a href="/facts/Thermodynamics/q4hIx3yP">thermodynamics</a>, an isobaric process is a type of <a href="/facts/Thermodynamic_process/LkeddKcu">thermodynamic process</a> in which the <a href="/facts/Pressure/eyc37GRG">pressure</a> of the <a href="/facts/Thermodynamic_system/VUr0kpWu">system</a> stays constant: ΔP = 0. The <a href="/facts/Heat/FjDGssCs">heat</a> transferred to the system does <a href="/facts/Work_(thermodynamics)/SjChajtw">work</a>, but also changes the <a href="/facts/Internal_energy/IYdsoxhR">internal energy</a> (U) of the system. This article uses the physics sign convention for work, where positive work is <a href="/facts/Work_(thermodynamics)/SjChajtw">work done by the system</a>. Using this convention, by the <a href="/facts/First_law_of_thermodynamics/hjL95WCr">first law of thermodynamics</a>,

Q
        =
        Δ
        U
        +
        W
        
      
    
    {\displaystyle Q=\Delta U+W\,}

where W is work, U is internal energy, and Q is heat. Pressure-<a href="/facts/Volume/aeAXCBUd">volume</a> work by the closed system is defined as:

W
        =
        ∫
        
        p
        
        d
        V
        
      
    
    {\displaystyle W=\int \!p\,dV\,}

where Δ means change over the whole process, whereas d denotes a differential. Since pressure is constant, this means that

W
 =
 p
 Δ
 V
 
 
 
 {\displaystyle W=p\Delta V\,}
 
.
Applying the <a href="/facts/Ideal_gas_law/Pphokwhf">ideal gas law</a>, this becomes

W
        =
        n
        
        R
        
        Δ
        T
      
    
    {\displaystyle W=n\,R\,\Delta T}

with R representing the <a href="/facts/Gas_constant/RUXszrMH">gas constant</a>, and n representing the <a href="/facts/Amount_of_substance/tQVyNLCp">amount of substance</a>, which is assumed to remain constant (e.g., there is no <a href="/facts/Phase_transition/eLP2BY8R">phase transition</a> during a <a href="/facts/Chemical_reaction/GpqWlKrz">chemical reaction</a>). According to the <a href="/facts/Equipartition_theorem/EJfmTK6W">equipartition theorem</a>, the change in internal energy is related to the temperature of the system by

Δ
 U
 =
 n
 
 
 c
 
 V
 ,
 m
 
 
 
 Δ
 T
 
 
 {\displaystyle \Delta U=n\,c_{V,m}\,\Delta T}
 
,
where cV, m is molar <a href="/facts/Heat_capacity/I63nzSyp">heat capacity</a> at a <a href="/facts/Constant_volume/K7kK0KwI">constant volume</a>.
Substituting the last two equations into the first equation produces:

Q
              
              
                
                =
                n
                
                
                  c
                  
                    V
                    ,
                    m
                  
                
                
                Δ
                T
                +
                n
                
                R
                
                Δ
                T
              
            
            
              
                Q
              
              
                
                =
                n
                Δ
                T
                (
                
                  c
                  
                    V
                    ,
                    m
                  
                
                +
                R
                )
              
            
            
              
                Q
              
              
                
                =
                n
                Δ
                T
                
                  c
                  
                    P
                    ,
                    m
                  
                
              
            
          
        
      
    
    {\displaystyle {\begin{aligned}Q&=n\,c_{V,m}\,\Delta T+n\,R\,\Delta T\\Q&=n\Delta T(c_{V,m}+R)\\Q&=n\Delta Tc_{P,m}\end{aligned}}}

where cP is molar heat capacity at a constant <a href="/facts/Pressure/eyc37GRG">pressure</a>.

Isobaric process open-in-new

Isobaric process