Work & Heat Transfer - Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

WORK AND HEAT TRANSFER

• Work done by the system is positive and when the work is done on a system, it is taken to be negative.
•  Work is a path function and inexact or imperfect differential.

•  For closed system and reversible process work done is calculated by ∫pdV.
•  In Cyclic Process:
•  For point function total change in property, in the cycle is zero.

ΔV=0, ΔP=0, ΔT=0, ΔU=0, Δh=0

• For path function net change in the cycle can may or may not be zero.

Work done in various reversible processes

Process Work done
(i) Constant pressure (isobaric) w_1-2 = p(v₂ – v₁) = mR (T₂ – T₁)
(ii) Constant volume (isochoric) w_1–2 = 0
(iii) Constant Temperature (isothermal)

(iv) Adiabatic (isentropic)

n = polytropic const.
m = no. of moles
g = Adiabatic constant

•  Mean effective pressure (P_m)

I_d — length of the p–v diagram along v–axis
a_d — area of the p–v diagram
k — Spring constant

•  Indicated power (for two stroke engine)

• Indicated power (for four stroke engine)

Brake power (BP) =

Mechanical efficiency

L — stroke of the piston
A — cross sectional area of the cylinder(πD²/4)

N — r.p.m of the crank shaft
n — number of cylinders
T — Torque on the crank shaft

• Mass Flow rate
  
  V — Velocity of flow
  v — Specific volume
  A — Cross sectional area

Flow work : The flow work in an open system represents the energy transfered across the system boundary as a result of the energy imparted to the fluid by a pump, blower or compressor to make the fluid across the control volume. It is analogous to
displacement work. Flow work per unit mass W_flow = PV
P — pressure
v — specific volume

•  Expansion of a gas against vacuum is called free expansion.
•  There is no work transfer involved in free expansion.
•  Heat flow out of a system is taken as negative while heat flow into a system is taken as positive.

• Heat like work is also a path function so is inexact or imperfect differential.

Specific heat c =
Heat capacity C = m.c

• For solids, specific heat does not depend on the process.
• The latent heat of fusion is the amount of heat transferred to melt unit mass of solid into liquid or to freeze unit mass of liquid to solid at a constant pressure and temperature.

F_Q = ml_F
l_F = Latent heat of fusion
• The latent heat of vaporisation is the amount of heat transferred to vaporize unit mass of liquid into vapour or condense unit mass of vapour into liquid at a constant pressure and temperature.