First law of thermodynamics ( closed system)

First law of thermodynamics ( closed system)
Constant Volume, Constant Pressure, Constant Temperature, Isentropic and Polytropic Process

1. 1.22 Basie concepts and rst law of thermodynamics

121 FIRST LAW OF THERMODYNAMICS - APPLICATION OF CLOSED
SYSTEMS (NON-FLOW PROCESS)
a. Constant Volume Process or Isochorie Process (V = constant):

constant volume process the
‘working substance is contained in a rigid
vessel, so that the boundaries of the
system are fixed and no work can be
done by the system, other than paddle-
‘wheel work input. It will be assumed that

“constant volume” implies zero work

vales stated ceberwie. Fig. 1.11 Constant volume process

According to First Law of Thermodynamics,
Q=W+AU

Net Work done, W = fy. PV
For constant Volume Process Vi =Vz. So that dV 0 and W -0.
Equation (1), Q = AU

Q=AU=mC, (TF; Ti)

b. Constant Pressure Process or Isobaric Process (p = constant):

It refers to the thermodynamic process in
‘which there is no change in pressure during the
process. Such type of processes is also known as
isobaric processes, To understand et us take a
cplindrical vesel having gas int. has a piston
above it, Piston is free to reciprocate in the
cylinder. Under normal station piston shall be PI =P2
subjected 10 atmosphere pressure. Now, lt heat

be added to cylinder from bottom of cylinder

Due to heat addition, presuming energy transfer

taking place reversibly and system always +
remaining in equilibrium, the gas shall wy to

expand. Expansion of gas results in ising up of Fi. 1.12 Constant pressure process
the piston and tartans a new state say 2

vv

2. 1.23 Basie concepts and first law ofthermodhmamies

‘The work involved in the raising of piston shall be given by.

W= fe Pav =P (VO

From the first law of thermodynamics. it can be given that,

dQ =dU+dw
lay fica

Qe MOT To +p (Va Vo
= mC(T2=T) +mR (TT)

mTi- Ti) (C#R) (Cp= Ce +R)

Qu: = mel)

©. Constant Temperature Process or Isothermal Process (T = pV = constant):

‘Thermodynamic process in which the
temperature remains constant is called
constant temperature or isothermal process.
In this case the gas or vapour may be
hheated at constant temperature and there
shall be no change in internal energy. The
work done will be equal to the amount of
heat supplied. The expansion of vapour is

not isothermal process, it is called as
Inperbolie process.
Pi pate Cons p= E Fig. 1.13 Constant Temperature
Process
According to First Law of Thermodynamics,
Qa-w+au

3. 1.24 Base concepts and first law of thermodynaniies

Net Work done, W= f pa

c
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sage
>
Ya
spills? (mec)

W=pV ne
Internal Energy, AU = mC\(T:—T))
For constant Temperature Process Tı “Tz, So that dT “0 and AU -0.
Equation (1), Q= W
Q-w

Y
AY in,

4. Constant Entropy Process or Reversible Adlabatic Process ( pV¥ = constant) :

An adiabatic process is one in which no
heat is transferred to or from the fluid during
the process. Such a process can be reversible
of irreversible, ie. during the process, Q = 0.
‘The adiabatic process follows the law pV! =
constant where y is called adiabatic index
and is given by the ratio of two specific
heats,

Fig. 1.14 Adiabatic Process

pv ©
PAV} =PaV = Constant. p=

According to First Law of Thermodynamics,
Q=W+au
During the process, Q = 0, W= — AU

Net Work done, W= ff pdV

4. 1.25 Basie concepts and first law of thermodynaniies

ian

Dalı- A)
ya

e. Polytropic Process ( p¥" = constant):

Polytropic process is the most
commonly used process in practice, In
this, the thermodynamic process is said to
be governed by the law pV" = constant
‘where n is the index which can vary from
— 2 to +. Figure 1.11 shows some

typical cases in which the value of n is

varied and the type of process indicated
for different values of n.

Fig. 1.15 Polytropie Process

PAV} = p2V3 = Constant, p

v

According to First Law of Thermodynamics,
Q=w+au a

CHERE) er)

Internal Energy, AU = mC\(T2~T))

Net Work done, W

Wenow tht, Gy -G=R y = E

5. 1.26 Basie concepts and first law of thermodynamics

DEV
Equation (1). Q= me (2) + E (Ti

In a polytropic process, the index n depends only on the heat and work

during the process (pV" = constant). The various processes considered earlier are
special cases of polytropie process for a perfect gas.

For example,
Whenn=0, DV =constan p= constant
When n=, pV = constant, pV = constant, ¥ mstant
Whenn=1, pV= constant, T= constant
Whenn=y pv? = constant, reversible adiabatic
Whenn=2, pv? = constant, Polytropic Process
index | PT Internat
Process Enthalpy Work Done | Heat
orn | relations Energy
Constant EE
A | mom | mom-T) o MC)
‘ons ey
O A mc—T)
EE PV = Pale o o ME png

temperature