What is Specific Heat at Constant pressure?
Specific heat at constant pressure (Cp) is a thermodynamic property that represents the amount of heat energy needed to raise the temperature of a unit mass of a substance by one degree Celsius (∘C) or one Kelvin (K), while keeping the pressure constant. Mathematically, it is expressed as:
Cp=ΔQ/m⋅ΔT
where:
- Cp is the specific heat at constant pressure,
- ΔQ is the heat added to the substance,
- m is the mass of the substance,
- ΔT is the change in temperature.
The specific heat at constant pressure is an important parameter in thermodynamics and is used to characterize the heat capacity of a substance under conditions of constant pressure. It is denoted in units of energy per unit mass per degree Celsius or Kelvin (e.g., Joules per gram per degree Celsius, J/(g·°C), or Calories per gram per degree Celsius, cal/(g·°C)).
For an ideal gas, the relationship between the specific heat at constant pressure (Cp), the specific heat at constant volume (Cv), and the gas constant (R) is given by:
Cp−Cv=R
This equation is a manifestation of the first law of thermodynamics, which relates the change in internal energy (U) to the heat added (Q) and the work done (W) on the system:
ΔU=Q−W
For an isobaric (constant pressure) process, the equation becomes:
ΔU=Qp−P⋅ΔV
Since W=−P⋅ΔV (work done on the system), and Qp is the heat added at constant pressure, the expression Qp−P⋅ΔV can be written as Qp, and this is related to the change in internal energy.
In summary, the specific heat at constant pressure is a crucial parameter in thermodynamics, providing insights into the heat transfer characteristics of a substance when its pressure is held constant.
What is Specific Heat at Constant Volume?
The specific heat at constant volume (Cv) is a thermodynamic property that represents the amount of heat energy needed to raise the temperature of a unit mass of a substance by one degree Celsius (∘C) or one Kelvin (K), while keeping the volume constant. Mathematically, it is expressed as:
Cv=ΔQ/m⋅ΔT
where:
- Cv is the specific heat at constant volume,
- ΔQ is the heat added to the substance,
- m is the mass of the substance,
- ΔT is the change in temperature.
The specific heat at constant volume is an important parameter in thermodynamics and is used to characterize the heat capacity of a substance under conditions of constant volume. It is denoted in units of energy per unit mass per degree Celsius or Kelvin (e.g., Joules per gram per degree Celsius, J/(g·°C), or Calories per gram per degree Celsius, cal/(g·°C)).
For an ideal gas, the relationship between the specific heat at constant volume (Cv), the specific heat at constant pressure (Cp), and the gas constant (R) is given by:
Cp−Cv=R
This equation is a manifestation of the first law of thermodynamics, which relates the change in internal energy (U) to the heat added (Q) and the work done (W) on the system:
ΔU=Q−W
For an isochoric (constant volume) process, the work done (W) is zero (W=0), and the equation becomes:
ΔU=Qv
Here, Qv represents the heat added at constant volume. In this case, the change in internal energy is equal to the heat added, as there is no work done against a changing volume.
In summary, the specific heat at constant volume is a fundamental thermodynamic property that characterizes the heat transfer characteristics of a substance when its volume is held constant.
Difference Between Specific Heat at Constant pressure and Specific Heat at Constant Volume?
The specific heat at constant pressure (Cp) and the specific heat at constant volume (Cv) are two thermodynamic properties that describe the amount of heat energy required to change the temperature of a substance under different conditions. Here are the key differences between Cp and Cv:
- Definition:
- Cp: Specific heat at constant pressure is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius or one Kelvin, while keeping the pressure constant.
- Cv: Specific heat at constant volume is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius or one Kelvin, while keeping the volume constant.
- Conditions:
- Cp: Applies to processes where the pressure of the system is held constant.
- Cv: Applies to processes where the volume of the system is held constant.
- Mathematical Relationship:
- For an ideal gas, the relationship between Cp, Cv, and the gas constant (R) is given by: Cp−Cv=R.
- This equation represents a fundamental relationship derived from the first law of thermodynamics and is valid for ideal gases.
- Work Done:
- Cp: Involves work done against a constant pressure during a process.
- Cv: Involves no work done against a constant volume during a process.
- Isochoric and Isobaric Processes:
- Cp: Relevant to isobaric processes (constant pressure).
- Cv: Relevant to isochoric processes (constant volume).
- Applications:
- Cp: Important in understanding heat transfer in processes occurring at constant pressure, such as combustion reactions.
- Cv: Important in understanding heat transfer in processes occurring at constant volume, such as certain laboratory experiments or reactions occurring in closed containers.
- Units:
- Both Cp and Cv are expressed in units of energy per unit mass per degree Celsius or Kelvin (e.g., Joules per gram per degree Celsius, J/(g·°C), or Calories per gram per degree Celsius, cal/(g·°C)).
In summary, Cp and Cv represent specific heat capacities under different thermodynamic conditions—constant pressure and constant volume, respectively. These properties are fundamental in understanding the thermal behavior of substances in various processes.
Frequently Asked Questions – FAQ’s
Why are Cp and Cv important in thermodynamics?
They are fundamental in understanding heat transfer characteristics during processes at constant pressure and constant volume, providing insights into the thermal behavior of substances.
What are the units for Cp and Cv?
Both Cp and Cv are expressed in units of energy per unit mass per degree Celsius or Kelvin (e.g., J/(g·°C) or cal/(g·°C)).
How are Cp and Cv measured experimentally?
They can be measured using calorimetry, where the heat added or removed during a process is measured along with the corresponding temperature changes.
In which processes is Cv relevant?
Cv is relevant in isochoric processes, where the volume is held constant.
In which processes is Cp relevant?
Cp is relevant in isobaric processes, where the pressure is held constant.
How do Cp and Cv relate to the first law of thermodynamics?
Cp−Cv=R is a relationship derived from the first law of thermodynamics, linking these specific heat values with the gas constant.
What is the key difference between Cp and Cv?
Cp applies to processes at constant pressure, while Cv applies to processes at constant volume.
What is specific heat at constant volume (Cv)?
Cv is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius or one Kelvin while keeping the volume constant.
How is Cp mathematically expressed for an ideal gas?
For an ideal gas, Cp−Cv=R, where R is the gas constant.
What is specific heat at constant pressure (Cp)?
Cp is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius or one Kelvin while keeping the pressure constant.
