DAY FOURTEEN
Thermodynamics
Learning & Revision for the Day
u Zeroth Law of u Thermodynamic Processes u Heat Engine
Thermodynamics u Second Law of Thermodynamics u Carnot Engine and Its
u First Law of u Reversible and Irreversible Efficiency
Thermodynamics Processes u Refrigerator
Zeroth Law of Thermodynamics
(Concept of Temperature)
When there is no exchange of heat between two systems placed in contact, then both
are called in thermal equilibrium.
According to this law, if two systems A and B , separated by an adiabatic wall, are
separately and independently in thermal equilibrium with a third system C, then the
systems A and B are also in a state of thermal equilibrium with each other.
C
A B
Adiabatic wall
Basic Terms Used in Thermodynamics
Heat It is the energy, which is transferred between system and surroundings due to the
temperature difference.
Internal Energy Internal energy of a system is defined as the sum of the total kinetic
energy of all its constituent particles and sum of all the potential energies of
interaction among these particles.
The internal energy of an ideal gas is totally kinetic and it is given by
3
U = µRT
2
3
and change in internal energy ∆U = µR∆T .
2
NOTE • For non-ideal gases, internal energy depends not only on the temperature but also on the
pressure.
, Work
T1>T2
Consider a system in a cylinder with movable piston, whose
volume can be changed (a gas, liquid or solid). Suppose, the p
cylinder has a cross-sectional area A and pressure exerted by T1
system on the piston face is p. T2
The work done by the system on the surroundings for small
displacement dx is dW = pAdx. V
Vf
p-V graph for isothermal process
W = ∫ dW = ∫ pdV
Vi Molar specific heat of a gas under isothermal condition
∆Q ∆Q
i.e. work done in a finite change of volume from Vi to V f . C= = =∞
m∆T m (0)
NOTE • Work done by the system depends on the initial and final dp p
states. Slope of p-V curve at any point is =− ⋅
dV V
• If volume of the system increases, then work is done by the
Work done in an isothermal process
system and it is taken as positive work done.
Vf Vf
• If volume of the system decreases, then work is done on ∆W = ∫ pdV = nRT ln
the system and it is taken as negative work done. Vi Vi
where, n = number of moles, R = gas constant
First Law of Thermodynamics and T = temperature.
V f and Vi are final and initial volume of the gas
According to this law, the heat given to a system (∆Q) is equal
respectively.
to the sum of increase in its internal energy (∆U) and the work
done (∆W ) by the system against the surroundings. As per first law of thermodynamics, since, ∆T = 0 , hence,
∆U = 0 for an ideal gas and we have ∆Q = ∆W .
Mathematically, ∆Q = ∆U + ∆W
Thus, heat supplied to the system in an isothermal
process is entirely used to do work against external
Sign Convention surroundings.
∆Q = + ve when heat supplied = − ve when heat is rejected
∆U = + ve when temperature increases 2. Adiabatic Process
= − ve when temperature decreases It is that process in which there is no exchange of heat of
∆W = + ve when work is done by the system (expansion) the system with its surroundings. Thus, in an adiabatic
= − ve when work is done on system (compression)
process p, V and T change but ∆Q = 0 or entropy remains
First law of thermodynamics is based on the energy ∆Q
conservation. constant ∆S = = 0 .
T
Thermodynamic Processes Q2 Q1
A thermodynamic process is the process of change of state of
a system involving change of thermodynamic variables, e.g. p Q1 > Q2
p, V , T etc.
When a system undergo a thermodynamic change, then work
done either by system on surrounding or by surroundings on
system is called external work. V
V2 p-V graph for adiabatic process
Wext = ∫ p dV = area under p-V curve.
V1 The equation of state for an adiabatic process is
pV γ = constant or T V γ − 1 = constant or T γ p1 − γ = constant
1. Isothermal Process
l
Molar specific heat of a gas under adiabatic condition
It is that process in which temperature remains constant.
Here, exchange of heat with the surroundings is allowed. ∆Q 0
C= = =0
As temperature T remains constant in an isothermal m ⋅ ∆T m ⋅ ∆T
process, hence as per Boyle’s law dp p
l
Slope of an adiabatic at a point is =−γ .
1 dV V
p ∝ or pV = constant
V
Thermodynamics
Learning & Revision for the Day
u Zeroth Law of u Thermodynamic Processes u Heat Engine
Thermodynamics u Second Law of Thermodynamics u Carnot Engine and Its
u First Law of u Reversible and Irreversible Efficiency
Thermodynamics Processes u Refrigerator
Zeroth Law of Thermodynamics
(Concept of Temperature)
When there is no exchange of heat between two systems placed in contact, then both
are called in thermal equilibrium.
According to this law, if two systems A and B , separated by an adiabatic wall, are
separately and independently in thermal equilibrium with a third system C, then the
systems A and B are also in a state of thermal equilibrium with each other.
C
A B
Adiabatic wall
Basic Terms Used in Thermodynamics
Heat It is the energy, which is transferred between system and surroundings due to the
temperature difference.
Internal Energy Internal energy of a system is defined as the sum of the total kinetic
energy of all its constituent particles and sum of all the potential energies of
interaction among these particles.
The internal energy of an ideal gas is totally kinetic and it is given by
3
U = µRT
2
3
and change in internal energy ∆U = µR∆T .
2
NOTE • For non-ideal gases, internal energy depends not only on the temperature but also on the
pressure.
, Work
T1>T2
Consider a system in a cylinder with movable piston, whose
volume can be changed (a gas, liquid or solid). Suppose, the p
cylinder has a cross-sectional area A and pressure exerted by T1
system on the piston face is p. T2
The work done by the system on the surroundings for small
displacement dx is dW = pAdx. V
Vf
p-V graph for isothermal process
W = ∫ dW = ∫ pdV
Vi Molar specific heat of a gas under isothermal condition
∆Q ∆Q
i.e. work done in a finite change of volume from Vi to V f . C= = =∞
m∆T m (0)
NOTE • Work done by the system depends on the initial and final dp p
states. Slope of p-V curve at any point is =− ⋅
dV V
• If volume of the system increases, then work is done by the
Work done in an isothermal process
system and it is taken as positive work done.
Vf Vf
• If volume of the system decreases, then work is done on ∆W = ∫ pdV = nRT ln
the system and it is taken as negative work done. Vi Vi
where, n = number of moles, R = gas constant
First Law of Thermodynamics and T = temperature.
V f and Vi are final and initial volume of the gas
According to this law, the heat given to a system (∆Q) is equal
respectively.
to the sum of increase in its internal energy (∆U) and the work
done (∆W ) by the system against the surroundings. As per first law of thermodynamics, since, ∆T = 0 , hence,
∆U = 0 for an ideal gas and we have ∆Q = ∆W .
Mathematically, ∆Q = ∆U + ∆W
Thus, heat supplied to the system in an isothermal
process is entirely used to do work against external
Sign Convention surroundings.
∆Q = + ve when heat supplied = − ve when heat is rejected
∆U = + ve when temperature increases 2. Adiabatic Process
= − ve when temperature decreases It is that process in which there is no exchange of heat of
∆W = + ve when work is done by the system (expansion) the system with its surroundings. Thus, in an adiabatic
= − ve when work is done on system (compression)
process p, V and T change but ∆Q = 0 or entropy remains
First law of thermodynamics is based on the energy ∆Q
conservation. constant ∆S = = 0 .
T
Thermodynamic Processes Q2 Q1
A thermodynamic process is the process of change of state of
a system involving change of thermodynamic variables, e.g. p Q1 > Q2
p, V , T etc.
When a system undergo a thermodynamic change, then work
done either by system on surrounding or by surroundings on
system is called external work. V
V2 p-V graph for adiabatic process
Wext = ∫ p dV = area under p-V curve.
V1 The equation of state for an adiabatic process is
pV γ = constant or T V γ − 1 = constant or T γ p1 − γ = constant
1. Isothermal Process
l
Molar specific heat of a gas under adiabatic condition
It is that process in which temperature remains constant.
Here, exchange of heat with the surroundings is allowed. ∆Q 0
C= = =0
As temperature T remains constant in an isothermal m ⋅ ∆T m ⋅ ∆T
process, hence as per Boyle’s law dp p
l
Slope of an adiabatic at a point is =−γ .
1 dV V
p ∝ or pV = constant
V
