define co-cv 11th phy 7th chapter
Answers
Answer:
Every molecule or a compound in a thermodynamic system has a different response to heat. A simple example to understand this is when a bucket of water and a piece of metal are placed in the scorching sun for 2 hrs, and temperatures of both are checked later. The temperature of the metal piece will be higher as compared to water; this is because water is resistant to minute changes in temperature and has a high heat capacity.
Heat capacity can be defined as the ratio of the amount of heat absorbed by a system to that of the change in temperature. This formula can be correlated with the above-stated example. The temperature change was the same for both the materials but the difference observed can be owed to its different heat capacity.
Heat capacity is measured using a calorimeter. It is important to note that the amount of heat required to raise the temperature of 1 mole of gas by 1 degree is called the molar heat capacity of the gas.
The formula for determining molar heat capacity:
C= q/ nΔT
The formula can be rearranged as q = n ×C ×ΔT
Here, q= the amount of heat supplied or absorbed by the system
n= number of moles of the gas
C= molar heat capacity
ΔT= Temperature change
Heat capacity is usually expressed in calories per degree.
Explanation:
What are Cp and Cv?
Cp is the term used to represent the molar heat capacity of a substance at constant pressure whereas, Cv is the term for molar heat capacity at constant volume. Thus, these two parameters define the molar heat capacity at varying pressure and temperature.
The formula for Cp and Cv can be derived from the formula for molar heat capacity
Cp= qp/ nΔT, which can be rewritten as qp = Cp × n × ΔT
Cv= qv/ nΔT, which can be rearranged as qv = Cv × n × ΔT
Relation between Cp and Cv for ideal gases:
Ideal gases are hypothetical gases that adhere to the following rules:
The ideal gas molecules do not interact with each other; the only interaction between them is in the form of an elastic collision.
Ideal gas molecules are considered as point molecules, having no volume of themselves.
The pressure and volume components of an ideal gas are represented by an ideal gas equation:
PV= nRT
Where, P= Pressure,
V= Volume
n= no of moles of an ideal gas
R= Gas constant
T= Temperature
A co-relation between Cp and Cv can be derived using the ideal gas equation and the previously derived equations for Cp and Cv.
Heat at constant pressure is given by the equation:
qp = Cp × n × ΔT = ΔH ……………………. (1)
The equation for heat at constant pressure is equal to the change in enthalpy, hence can be denoted as ΔH
Heat at constant volume is given by the equation:
qv = Cv × n × ΔT = ΔU …………………….(2)
This equation of heat at constant volume is equal to the internal energy change (ΔU ) experienced by the thermodynamic system.
According to the first law of thermodynamics,
ΔH= ΔU + PΔV …………………………….(3)
Now, for one mole of an ideal gas, the ideal gas equation can be written as:
PΔV= RΔT ………………………………….. (4)
Substituting equation (4) in (3)
ΔH= ΔU + RΔT………………………………(5)
On substituting the equations (1) and (2) in place of ΔH and ΔU in equation (5), we get,
Cp × n × ΔT= Cv × n × ΔT + RΔT…………….(6)
Dividing the entire equation (6) by ΔT and taking n=1, as the equation is for one mole of an ideal gas. The equation becomes,
Cp= Cv + R
Cp-Cv= R
The above equation shows the correlation between the molar heat capacity at constant pressure and molar heat capacity at constant volume. Thus, the difference between the two parameters Cp and Cv for a substance is equal to the universal gas constant.
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