Sensible and Latent Heat

Sensible and Latent Heat

It is known that a substance can exists in three phases namely solid, liquid and gas. When a substance is heated or cooled temperature of the substance increases or decreases respectively unless there is any phase change. Quantity of heat added or removed to change the temperature by unit degree is known as specific heat. For solids and liquids same quantity of heat is required to cause unit degree rise for both constant pressure heating as well as constant volume heating as they are incompressible. But for gases there is appreciable difference in the quantity of heat required to cause unit difference in temperature between constant volume and constant pressure processes. Accordingly, they are known as specific heat at constant volume (C_V) and specific heat at constant pressure (C_P). Thus to increase the

temperature of m kg of the given substance by DT degree, amount of heat required is given by

Q =mCvDT at Constant Volume                        ...(2.5)

Q₁ =mC_PDT at Constant Pressure                 …(2.6)

If a certain single component system is undergoing phase change at constant pressure, temperature of the system remains constant during heating or cooling. Quantity of heat removed or added to cause the change of phase of unit mass of the substance is known as latent heat. For example latent heat of fusion of water is the amount of heat to be removed to solidify 1 kg of water into 1 kg of ice at a given temperature.

Let us consider a process of converting 1 kg of ice at -30°C to system to steam at 250°C at atmospheric pressure. We know that ice melts at 0°C and water evaporates at 100°C at atmospheric pressure.

For a constant rate of heating, if temperature at different instants are plotted we will get a graph as shown in Figure 2.9.

Figure 2.9 Illustration for sensible and latent heat        

The total heat required can be obtained as follows:      

          Q  = Qab + Qbc + Qcd + Qde + Qef ...(2.7)

          Q_ab = mCice (t_b - t_c)        ...(2.8)

Qbc   =  Latent heat of melting of ice at 0^oC       

          Q_cd = mC_water (t_d - t_c)       ...(2.9)

Qde   = Latent heat of evaporation of water at 100^oC  

          Qef = mC_PSteam (t_f - t_e)     ...(2.10)

Where C_ice =Specific heat of ice        

C_water = Specific heat of water 

C_PSteam =Specific heat of steam at constant pressure

Reversible Adiabatic Process

A reversible process during which, the system and the surroundings do not exchange any heat across the boundary is known as reversible adiabatic process. For such a process, pressure and volume variation is governed by the law :

pV =constant                          . ..(2.11)

Where

C_p is the specific heat at constant pressure

C_V is the specific heat at constant volume

Detailed discussion on these specific heats is presented in the next chapter.

A wall which does not permit the heat flow across it is known as adiabatic wall, whereas the wall that permits the heat is known as diathermic wall. In an adiabatic process the only possible energy interaction across the boundary of the system is work transfer to or from the system.

Displacement work involved in a reversible adiabatic process can be expressed as

Comparison between work and heat

^l  Both heat and work are boundary phenomena, that is, they occur only at the boundary.

^l       The interaction due to the temperature difference is heat and all other interactions are to be taken as work.

^l      Both work and heat are path functions, that is, they are inexact differentials.