Heat Capacity of a Substance
The heat capacity of a substance, commonly abbreviated as thermal capacity (capital C), is a measure of the amount of heat needed to change the temperature of the substance by a specific amount. Heat capacity is measured in SI units and is referred to as the joules per kelvin (J/K) unit.
In a heat capacity calculation, the amount of heat energy transferred to an object (symbol C) is proportional to the amount of temperature increase that results.
\[C=Q\Delta T.C=Q\Delta T\].
A system's heat capacity scales with its size since it is an extensive property. When a sample contains twice as much substance as another, it takes twice as much heat (Q) to achieve the same temperature change (ΔT). It would take 2,000 J to heat a second iron block with twice the mass of a first iron block if it took 1,000 J to heat a block of iron.
The Measurement of Heat Capacity
It is not always possible to predict the capacity of a system in terms of heat. This depends more on the state variables of the thermodynamic system under discussion. The amount of change in volume or pressure is dependent upon many factors, including the temperature itself, the pressures that are in the system, and how those pressures have changed while the system has been going from one temperature to another. Unlike pressure-volume work done on the system, pressure-volume work done on the system absorbs heat without raising its temperature. This is because pressure-volume work on the system raises its temperature by a mechanism other than heating. It is because of this temperature dependence that a calorie is formally defined as the energy required to heat 1 g of water from 14.5 to 15.5 degrees Celsius instead of generally by just 1 degree Celsius.
Therefore, different methods can be used to determine heat capacity, most commonly at constant pressure and volume. To indicate the meaning of the measured value, the subscripts (p and V, respectively) are usually used. Typically, gas and liquid measurements are also based on constant volume. As the temperature increases, the substance expands against the constant pressure as it is measured at constant pressure. Therefore, the constant pressure measurements are greater than those at constant volume. In gases, significantly greater values are typically found under constant pressure than under constant volume, especially for gases at constant pressure.
Molar Specific Heat Capacity at Constant Pressure: If the heat transfer to the sample takes place at the same pressure as the sample remains, this method is known as Molar Specific Heat Capacity at Constant Pressure.
Molar Specific Heat Capacity at Constant Volume: If the sample is converted to heat by keeping its volume constant, the actual heat produced by this process is known as Molar Specific Heat Capacity at Constant Volume.
Points to Consider
Mass and volume are irrelevant for the specific heat capacity as opposed to the total heat capacity. In order to raise the temperature of a given substance by one degree Celsius, the amount of heat it takes to warm that mass by one degree Celsius. Special heat capacity is measured in J/(kg °C) or equivalently in J/(kg K).
C=cm or c=C/m is the relationship between the capacity for heat and the specific heat.
The mass m, specific heat c, change in temperature ΔT, and heat added (or subtracted) Q are related by the equation: Q=mc Temperature and phase of substances have an effect on specific heat values. Since they are difficult to calculate, they are measured empirically and available in tables as references.
Key Terms
In thermodynamics, specific heat capacity can be defined as the amount of heat needed to raise or lower the temperature of a unit mass of a substance by one degree Celsius. Specifically, it is a property of intensities.
FAQs on Specific Heat of Constant Pressure
1. Why Specific Heat of a Gas at Constant Pressure is always Greater than the Specific Heat of a Gas at Constant Volume?
CP is higher than CV because when the gas is heated at constant volume, no external work is done and the heat supplied is consumed only by increasing the internal energy of the gas. Yet if the gas is heated at constant pressure, the gas will expand against the external pressure, and some additional work will be performed. In this case, the heat is used to increase the internal energy of the gas and to perform some external work.
Since the internal energy depends only on the temperature, the internal energy of the gas mass will increase by the same amount, whether the pressure or volume remains constant, at the same temperature increase. But since external work is additionally done at constant pressure than at constant volume to produce the same increase in gas temperature.
2. Can you tell me what the Specific Heat is at Constant Volume?
According to the specific heat formula, one degree K of temperature increase per unit mass of an object requires one degree K of energy. However, the situation is more complicated than that. There are several factors that determine how much energy is required. Specifically, will the volume of the object remain the same when heated, or will the pressure on it remain the same? Whether the volume remains the same or the pressure remains the same, the heat specific to the object will change. At constant volume, it is called specific heat, while at constant pressure, it is called a specific heat at constant pressure. When heated at constant pressure, the object does not affect its surroundings, whereas, at constant pressure, the object does.
3. What is Specific Heat Capacity and Heat Transfer?
The heat Q transferred to cause a temperature change depends on how large the temperature change is, the mass of the system, and the substances and phases involved.
A change in temperature directly corresponds to a change in heat transfer. It is necessary to add twice as much heat to a mass m in order to double the temperature change.
In addition, the mass directly influences the amount of heat transferred. The heat needed to cause an equivalent temperature change in a doubled mass would be twice as much.
The amount of heat transferred is dependent on the nature of the substance and its phase. The same amount of heat required to cause a temperature change in a mass of copper will require 10.8 times the amount of heat required to cause an equivalent temperature change in a mass of water, assuming that neither substance undergoes a phase change.
4. Mayer's formula?
It depends on the mass of the system, the number of substances and phases involved, as well as the temperature change, how much heat Q it takes to cause a temperature change.
When the temperature changes, the heat transfer changes as well. In order to double the change in temperature, a mass m must be heated twice as much.
Additionally, the mass directly influences the amount of heat transferred. For a doubled mass to experience the same temperature change, it would require twice as much heat.
According to the nature of the substance and its phase, the amount of heat transferred varies. In order to cause an equivalent temperature change in a mass of copper, the same amount of heat will need to be applied 10.8 times more than to a mass of water, considering neither substance undergoes phase transitions.
