Short Notes: Calculation of Work and Heat in Various Processes | Short Notes for Mechanical Engineering PDF Download

 Page 1


Calculation of Work and Heat in Various Processes
Work Done in Moving the Boundaries of a Closed System
Suppose a gas contained in piston cylinder expands from position 1 to 2, then work 
done by the gas
• Constant Volume Process (Isochoric Process):
° In isochoric process, volume is constant during process.
° Work done: dW = pdV = 0 
o Heat supplied to system: dQ = mCvdt
o AQ = mCv(T2-Ti) Where, Cv = Specific heat for constant volume process.
+
p
Pislon cylinder 
expands from t to 2
t
2
P
Constant pressure 
process
Change in internal energy of system:
dU = mCv dt 
A U = mCv(T2-Ti)
Page 2


Calculation of Work and Heat in Various Processes
Work Done in Moving the Boundaries of a Closed System
Suppose a gas contained in piston cylinder expands from position 1 to 2, then work 
done by the gas
• Constant Volume Process (Isochoric Process):
° In isochoric process, volume is constant during process.
° Work done: dW = pdV = 0 
o Heat supplied to system: dQ = mCvdt
o AQ = mCv(T2-Ti) Where, Cv = Specific heat for constant volume process.
+
p
Pislon cylinder 
expands from t to 2
t
2
P
Constant pressure 
process
Change in internal energy of system:
dU = mCv dt 
A U = mCv(T2-Ti)
Constant Pressure Process (Isobaric Process):
• In isobaric process, pressure is constant throughout process
• A1 / 1 / = P2^2 — P7I/7 = rnR (T^T-j)
• AQ = mCp(T2-Ti)
• AU = mCv(T2-T-,)
Constant volume 
heating process
Constant Temperature (Isothermal Process):
1
2
• In isothermal process, temperature is constant during process.
• If an ideal gas follows a constant temperature process, then Boyle’s law is
pV = constant
_ r r = p ,r ,/ n ii
- vx
or
K
.iry=m Jtr in—
K
Isothermal process
= 0 (as T2 =T x)
V 7 / T *
LO — _TT = In - ^ = In - ^ = wRZVk - -
. . . j/ - * - f' fj
Reversible Adiabatic Process:
In reversible adiabatic process there is no heat transfer between the system and 
the surrounding (Q = 0)
pVY = constant,
Where, r = adiabatic index, and Cp = specific heat for constant pressure
Page 3


Calculation of Work and Heat in Various Processes
Work Done in Moving the Boundaries of a Closed System
Suppose a gas contained in piston cylinder expands from position 1 to 2, then work 
done by the gas
• Constant Volume Process (Isochoric Process):
° In isochoric process, volume is constant during process.
° Work done: dW = pdV = 0 
o Heat supplied to system: dQ = mCvdt
o AQ = mCv(T2-Ti) Where, Cv = Specific heat for constant volume process.
+
p
Pislon cylinder 
expands from t to 2
t
2
P
Constant pressure 
process
Change in internal energy of system:
dU = mCv dt 
A U = mCv(T2-Ti)
Constant Pressure Process (Isobaric Process):
• In isobaric process, pressure is constant throughout process
• A1 / 1 / = P2^2 — P7I/7 = rnR (T^T-j)
• AQ = mCp(T2-Ti)
• AU = mCv(T2-T-,)
Constant volume 
heating process
Constant Temperature (Isothermal Process):
1
2
• In isothermal process, temperature is constant during process.
• If an ideal gas follows a constant temperature process, then Boyle’s law is
pV = constant
_ r r = p ,r ,/ n ii
- vx
or
K
.iry=m Jtr in—
K
Isothermal process
= 0 (as T2 =T x)
V 7 / T *
LO — _TT = In - ^ = In - ^ = wRZVk - -
. . . j/ - * - f' fj
Reversible Adiabatic Process:
In reversible adiabatic process there is no heat transfer between the system and 
the surrounding (Q = 0)
pVY = constant,
Where, r = adiabatic index, and Cp = specific heat for constant pressure
V ---?
Reversed adiabatic 
process
w _ P J\~ P J\ _ mRlTi ~ Ti 1
“ - - 1 - -1
AQ = 0 (No heat transfer from surrounding)
AU = -AW, (0 = AU + AW)
Reversible Polytrophic Process:
• In polytropic process, both heat and work transfers take place.
• The process equation is represented by p.Vn = C where n is called the index of 
process or polytropic index.
_ RVj-p;!', _ m R\T^ -T..'\ 
n — 1 n — 1
= m Cr 17, — 7, )
_ r —n
AO — --------x A T T
- - -1
where, n = polytropic index
Reversible polytropic 
process