HEAT AND THERMAL ENERGY: Specific Heat vs. Specific Heat Capacity

Although similar, the terms “ specific heat “ and “ specific heat capacity “ are not synonymous. Different materials have different abilities to absorb and store heat energy ( J ). Specific heat capacity refers to the amount of heat energy needed to raise 1 kilogram ( kg ) of a specific substance by 1 Kelvin ( K ). Please note, however, that the following forms of the specific heat capacity ( c ) equation are also used across various scientific disciplines:

c₁ = ( cal / g*℃ )

c₂ = ( kcal / kg*℃ )

c₃ = ( J / kg*℃ )

Regardless of which form we encounter, it is important to know that the temperature terms used actually refer to changes in temperature of a substance under observation; thus, a more general yet useful form of ( c ) is as follows:

c = ( Q / mΔT )

In this expression, heat is denoted with the letter ( Q ), mass with ( m ), and change of temperature with ( ΔT ). Although the terms “ heat “ and “ temperature “ are used interchangeably at times, they are in fact related yet different entities. Heat is a form of vibrational energy, whereas temperature describes a concentration of heat energy within a given region. On any given winter day, the temperature within most homes is much greater than that of any comparable region of space outdoors; however, the total quantity of heat energy contained within a square mile of a heated home is much, much greater in magnitude, even on the coldest of days.

Experimental data has been used to obtain values of specific heat capacity for many types of materials. For example, if equal quantities of several different substances are placed by a hot fireplace for equal periods of time, drastically different changes in temperature will occur. Under such conditions, an equal mass of iron will experience a change in temperature that is greater than that of water by a factor of 10!!!

A technique used in past times to study the behavior of heat within materials was referred to as “ mixing “. This technique preceded the calorimetry techniques commonly used in today’s introductory chemistry and physics laboratory experiments. When mixing is employed as an experimental tool, equal amounts of a particular substance are mixed together after hot and cold temperatures have been established within each sample. For example, if a given mass of water with a temperature of 5.0 ℃ is mixed with an equal quantity of water with a 95 ℃ temperature, the temperature of the final solution will be midway between these two extremes. This observation is in perfect agreement with the Law of Conservation of Energy: 

ΔT_c = ( 95 ℃ – 5.0 ℃ )

ΔT_c = 90 ℃

Theory predicts that the temperature of the colder quantity of water will increase by 45 ℃, while the temperature of the hot sample will decrease by 45 ℃ until the solution reaches an equilibrium temperature of 50 ℃. This is indeed the observation that is made when such experiments are carried out. The quantity of heat lost or gained is summed up with expressions that will reflect whether or not heat has been lost or gained during the experiment:

Hot System:

Q₁ = cm₁( Tf₁ – Ti₁ )

Ti₁ > Tf₁ 

Thus, Q₁ will have a negative value.

Cold System:

Q₂ = cm₂( Tf₁ – Ti₁ )

Tf₁ > Ti₁

Thus, Q₂ will have a positive value.

To the contrary, specific heat refers to a quantity of heat energy needed to change the temperature of a specific object of known mass by 1 ℃. For example, different quantities of energy will be needed to change the temperature of a 210 g block of aluminum as opposed to a single gram of it. The specific heat of an object is derived via usage of specific heat capacity data that was previously discussed:

Specific Heat Capacity of Aluminum: 0.891 J / g*℃ 

Specific Heat Capacity x Mass = Some value in units of ( J / ℃ )

( 0.891 J / g*℃ )( 210 g ) = 187.11 J / ℃

Thus, if the aforementioned block of aluminum increases by 1 ℃, we know that it absorbed 187.11 J of heat energy. This is drastically different from the quantity of heat energy needed to raise a 1.0 g aluminum container by 1 ℃ ( 0.891 J ). Accordingly, the formula for specific heat does not contain a term for mass: 

Q = cΔT

The practicality of this lattermost expression is most notable in industry. When a container of fixed mass has routine chemical reactions carried out within it, it would be cumbersome to use the expression for specific heat capacity over, and over, and over again in calculations. Once the simpler specific heat value has been determined for the system at hand, it is used for purposes of convenience.

Q: A copper pot has a mass of 0.5 kg, and its current temperature is 100 ℃. How much heat must be removed from it to establish a temperature of 0 ℃?

A: We first obtain the value of specific heat capacity for copper:

c_cu = ( 390 J / kg*K )

We next obtain a value of specific heat for the pot at hand:

( 390 J / kg*K )( 0.5 kg ) = 195 J / K

Oops!!! 

We are in need of Kelvin temperature ( T_k ) values. Fortunately, changes in temperature on the Kelvin and Celcius scales are synonymous; therefore, we only need to substitute ( K ) for ( ℃ ) in our calculations:

ΔT_c = ( T_f – T_i  )

ΔT_c = ( 0 ℃ – 100 ℃ )

ΔT_c = ( – 100 ℃ )

Therefore,

ΔT_K = ( – 100 K )

And,

Q = ( 195 J / kg*K )( – 100 K )

Q = – 19.5 kJ ≅ – 20 kJ