What is Molar Specific Heat? 

Heat capacity is the amount of heat energy absorbed or released by a chemical substance per the change in temperature of that substance. The change in heat is also called enthalpy. The SI unit of heat capacity is Joules per Kelvin, which is (J K^-1) 

Specific heat is generally the amount of heat required to increase the temperature of one gram of a substance or one unit of mass by one degree Celsius. The SI unit of specific heat is joule per Kelvin per kilogram that is (J kg^-1 K^-1). Specific heat changes according to the nature of the chemical substance. 

Molar specific heat is the amount of heat required to increase the temperature of one mole of a substance by one degree Kelvin (1 K) or Celsius (1°C). Molar specific heat is also known as molar heat capacity. The SI unit of molar specific heat is joule per mol per Kelvin that is J mol^-1K^-1 

Ever wondered why the sand and the salty water in the sea are at different temperatures, even though they are lying under the same amount of sun’s burning and scorching heat during the daytime? Does this question made you think and scratch your mind a little? Here is the answer for it, the science of specific heat. 

Specific Heat 

Specific heat is the quantity or amount of heat energy required to increase the temperature of one unit mass of the given chemical substance solid, liquid by 1 degree Celsius(1°C) or 1 Kelvin(1K). Scientifically the amount of heat energy to raise the temperature of 1kg of the given chemical compound or substance by 1°C or 1K is the specific heat of the chemical substance. 

The equation for the specific heat capacity can be written as,  

$\begin{array}{l}\text{Specific heat capacity}\left(C\right)=\frac{\Delta Q}{m\times \Delta T}\\ \text{Or},\Delta Q=C\times m\times \Delta T\end{array}$

• ΔQ= amount of heat energy required in joules 
• m = mass of the substance (kg) 
• ΔT = change in temperature in kelvin 

The SI unit of specific heat is J kg^-1 K^-1  

Therefore, the water and sand are at different temperatures even under the same condition. This is due to the fact that the specific heat of water is more than the specific heat of sand. This means that more heat needs to be supplied to raise the temperature of water than that of sand. 

Molar Specific Heat  

Now that we have understood the science of specific heat let us try to understand the science of molar specific heat.  

Molar specific heat is the amount of energy required to raise the temperature of one mole of the given chemical substance by 1 degree Celsius(1°C) or 1 Kelvin(1K). 

Molar Specific Heat Capacity $C_m=\frac{\Delta Q}{n\times \Delta T}$

Or, $\Delta Q=C_{m}n\times \Delta T$

ΔQ= amount of heat energy required in joules 

n= no. of moles 

ΔT =change in temperature in kelvin 

The SI unit of molar specific heat is J mol^-1 K^-1 

The relation between molar heat capacity and specific heat is stated below 

$C_m=\frac{C}{n}$

The molar specific heat of any substance can be measured similar to the specific heat measurement. 

Specific Heat at Constant Pressure or Volume 

• Specific heat of the substance can be calculated by heating the substance at constant volume. This is the specific heat at constant volume. It is denoted as C_V. 
• Specific heat of the substance can be calculated by heating the substance at constant pressure. This is the specific heat at constant pressure, denoted as C_P. 

The method of heating the gas determines the change in pressure/ volume with temperature, and the molar specific heat capacity. This can be shown by using different values of P (pressure) and V (volume) while heating the gas. 

This is the reason of infinite values for specific heat of the gas. The specific heat of a given substance would be constant only if a constant amount of heat is supplied. Thus, we have a particular value of specific heat at constant pressure (C_P) and at constant volume (C_V). 

 C_P – C_V = nR 

where n is the amount of substance, and R=8.3144598(48) J mol⁻¹ K, is the molar gas constant. This equation corresponds to ideal gases whereas the values for real gases is close to this but a little bit higher. The value of C_V,m is usually less than the value of C_P,m, where the subscript ‘m’ stands for molar heat capacities. This difference is mainly observed in the gases where C_P values are typically 30% to 66.7% greater than C_V values. 

Applications 

• The utensils used for cooking use a material of low specific heats so that the get heated up quickly. Mainly they have aluminium or copper polished bottoms. The handles of such utensils are made of high specific heat material to sustain the heat and to save our hands. 
• Insulators use materials of high specific heat. So, houses made of wood are more suitable to live in high temperature areas. 
• Due to a high specific heat of water, in swimming pool, water is found to be cool as compared to the temperature outside. 

Molar Heat Capacity of Monatomic Gases 

The temperature of a sample of a substance reflects the average kinetic energy of its constituent particles (atoms or molecules) relative to its center of mass. According to quantum mechanics, at room temperature and ordinary pressures, an isolated atom in the gaseous phase does not store any significant amount of energy except in the form of kinetic energy. Therefore, if we provide a certain amount of heat energy, ΔQ to N number of atoms of a monatomic gas, in a container of fixed volume, the kinetic energy of each atom will increase independently of the atom's mass. This increase is by the factor of ΔQ/N. This assumption forms the basis of the theory of ideal gases. 

Context and Applications   

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for  

• Bachelors in Science (Physics)  
• Masters in Science (Physics)