# What Is Molar Heat Capacity And How Do You Calculate It?

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**By dividing heat capacity by the total number of moles, the molar heat capacity—the quantity of heat needed to raise the temperature of 1 mole of a substance by 1 unit—is determined.**

Have you ever wondered why using a pan doesn’t cause us to burn ourselves?

Of course, the handle shields us, but why doesn’t it heat up to the same temperature as the pan? It receives the same amount of heat exposure after all.

A panhandle is a poor heat conductor since, in most cases, it is made of plastic. The temperature rise of the plastic handle is also much smaller than that of the metal section when exposed to the same quantity of heat. This is explained by the handle’s higher heat capacity than the metal used to make the pan.

The quantity of heat energy needed to increase a given mass of a substance’s temperature by one unit is known as its heat capacity. Properties obtained from a material’s heat capacity include specific heat capacity and molar heat capacity.

## Specific heat & Molar specific heat

Heat capacity is a complex characteristic; as such, it is influenced by the quantity and size of the substance. Physics frequently makes use of a modified concept known as specific heat capacity or simply specific heat. Specific heat is a more useful attribute because it is independent of the amount of the substance.

The amount of energy needed to raise a substance’s mass by one unit of temperature is known as its specific heat. It is mathematically defined as a substance’s heat capacity divided by its mass. Calculating specific heat is as follows:

Here, c is measured in J/kg and stands for specific heat.

A substance’s heat capacity is measured in J/K, while its mass is measured in kilogrammes. A further crucial formula for expressing specific heat is:

This time, c stands for specific heat, Q speaks for the difference in heat energy in joules, m stands for the substance’s mass, and T stands for the difference in temperature in Kelvin.

It is much simpler to further change the definition and formula of heat capacity to include moles as the amount of a chemical is typically measured in moles, not grammes, in chemistry.

The amount of heat needed to elevate 1 mole of a substance by 1 Kelvin is known as the molar heat capacity. Similar to specific heat, the molar heat capacity is an intense attribute, meaning that it is unaffected by the quantity of a substance.

It is defined mathematically as: The heat capacity of a substance divided by the number of moles

Here, C is heat capacity (J/K), n is the number of moles, and cm is the molar heat capacity (J/K.mol) (mol).

Although the amount or size of the substance may not affect specific heat or molar heat capacity, the values of these quantities can change depending on how they were calculated.

When a substance, especially a gas, receives heat energy, the temperature rises along with an increase in either volume or pressure, and occasionally both. Both Gay-law Lussac’s and Charles’ law can be used to explain these phenomena.

Molar heat capacities measured at constant pressure (isobaric) and constant volume are frequently represented by the symbols C_{P,m} and C_{V,m} (isochoric).

Molar specific heat is always higher measured at constant pressure than it is at constant volume. This is so that heat can be used to create work and expand volume while being delivered at a steady pressure. In contrast, heat delivered at a constant volume is fully utilised to raise the substance’s temperature.

The heat capacity ratio, often known as the adiabatic index (γ = C_{P}/C_{V}), is a crucial concept when dealing with reversible processes in thermodynamics. The universal gas constant R, on the other hand, is equal to the difference between C_{P,m} and C_{V,m}. Mayer’s relation can be defined as C_{P,m }– C_{V,m} = R.

## How can one determine a substance’s molar heat capacity?

It’s not very complicated to determine a substance’s heat capacity, specific heat, and molar heat capacities.

The quantities (amount of heat given or removed, initial temperature, final temperature, mass, and number of moles of the substance) can be found individually and then substituted in the appropriate locations in the formulas to determine the values.

### Step 1: Finding heat capacity

The quantity of heat needed to increase the temperature of a certain quantity of a substance by one unit is known as its heat capacity. The definition is stated as follows:

In this case, C stands for heat capacity, Q for heat energy, and ΔT for temperature differential. ΔQ is an alternative to Q.

ΔT is defined as T1-T2, where T1 denotes the substance’s initial temperature and T2 its final temperature. Start by using a thermometer to record T1’s initial or starting temperature. Moreover, weigh the sample (m) and record the weight in kg for future reference.

Next, give the system a predetermined amount of heat energy (Q). Either joules or calories can be used to express the amount of heat energy. Wait for the temperature to stabilise when you’ve finished providing heat, then record the ultimate temperature as T2.

By multiplying the Celsius value by 273.15 (zero degrees Celsius = 273.15 Kelvin), you can convert a temperature value. If the amount of delivered heat energy is given in calories, convert it to joules. To convert heat energy from calories to joules, multiply the number by 4.184 (1 cal = 4.184 joules).

Lastly, change the Q, T1, and T2 numbers in the heat capacity formula. To calculate and determine the sample’s heat capacity, grab a calculator or use your head. Heat capacity is measured in J/K units.

### Step 2: Identifying a specific heat source or heat capacity

By dividing the sample’s heat capacity by its mass (c = C/m), it is simple to determine the specific heat capacity or specific heat. To determine the sample’s specific heat, divide the value of C from the previous step by the value of m that was also noted there. The final quantity will be expressed in units of J/kg.K.

### Step 3: Determining molar heat capacity

The term “n” denotes the number of moles of the sample, and it can be found in the formula for molar heat capacity (cm= C/n) if you scroll back up. Divide the sample’s quantity by its molar mass to obtain the number of moles.

You may now determine molar heat capacity by replacing the value of heat capacity (C) and the number of moles (n) in the formula.

By dividing the sample’s specific heat (c) by its molar mass, one can obtain the molar heat capacity (M). Make sure to convert the molar mass to kg/mol when doing this.

## Alternative Method – Using a calorimeter

Using a calorimeter is another approach for figuring out a substance’s specific heat. A calorimeter is a piece of scientific equipment that includes, among other things, an inner and outer vessel, a stirrer, a thermometer, and insulation.

The sample material whose specific heat needs to be calculated is inside the inner vessel or cup. It is positioned in the centre of the water-filled outer vessel.

The mass and beginning temperatures of the water and the sample stuff are noted as the operation begins.

After that, ignition wires are used to heat the sample. Heat transmission between the two starts as soon as the sample’s temperature exceeds that of the surrounding water. The water and sample are then tested at their final temperatures after the electric flow has been switched off for a while. The sample material will lose the same amount of heat energy that the water in the external vessel gains when heated. We now apply the equation Q = mcT.

For the sample, ΔQ_{s}= (mcΔT)_{s}, and for the water, ΔQ_{w}=(mcΔT)_{w}.

But ΔQ_{s }= ΔQ_{w}. Thus, (mcΔT)_{s }= (mcΔT)_{w}.

Substitute the values for the mass of the sample and the water (m_{s} and m_{w}, respectively), the change in temperature (ΔT_{s} = T1_{s}-T2_{s }and ΔT_{w} = T1_{w}-T2_{w}), and the specific heat of water (c_{w}) as 4.1796 kJ/kg.K to determine the specific heat of the sample (c_{s}).

Once the substance’s specific heat is found, multiplying it by its molar mass will provide you with the molar heat capacity of the substance.