ENGR-1100 Introduction to Engineering Analysis

1
Lecture 1 Laws of Thermodynamics

• Thermodynamic state - equilibrium
• Thermodynamic processes
• Laws of thermodynamics
• Absolute Temperature
• Problems 2.5, 2.6, 2.8

2
Thermodynamic state - equilibrium

• Thermodynamic intensive coordinates are uniform
  across the whole system (T, P, ?) or across each
  macroscopic phase (e.g., water and ice density
  density at the melting point.
• All thermodynamic coordinates are time
  independent
• Mechanical equilibrium, thermal equilibrium and
  chemical equilibrium

3
Macroscopic vs. microscopic state

• Thermodynamic coordinates (T, P, ?) define
  macroscopic state of equilibrium.
• Microscopic state is defined by atomic positions,
  and momenta - many microscopic states are
  consistent with a macroscopic state
• Statistical mechanics connects microscopic
  description and detail with macroscopic state via
  ensemble average

4
Thermodynamic process ? change of the
thermodynamic state

• Infinitesimal process ? infinitesimal change of
  coordinates, e.g., dT, dV, dP
• Quasi static process ? always near equilibrium
• Adiabatic process ? no heat
• Reversible process ? can be restored to the
  initial state without charging surroundings

5
0th law of thermodynamics
Two or more systems in equilibrium do not exhibit
heat flow among each other, they are at the same
temperature Later we will see that criterion of
equilibrium for isolated system, i.e., const E,
V, T is the maximum entropy state dS(E, V, N) 0
dS dS1dS2 0
Allowing only energy exchange between two
isolated systems
From conservation of energy
6
1st law of thermodynamics - conservation of energy

• dE dQ-dW
• d indicates inexact differential - depends on the
  integration path
• In a cycle, ?E 0
• net Q in net W out
• Work and heat are not state functions
• Energy is a state function
• dW Fdx can be PdV, -?dl, -?it

7
2nd law of thermodynamics - entropy
For a reversible process dQ TdS Where S is
entropy which a state function, and T is an
absolute temperature The entropy can by
calculated by integrating heat over a reversible
path
8
Absolute temperature
Consider the Carnot cycle
Since entropy is the state function
Q1
T1
T2
Q2
Using reference T3 273.16 K
Q gt 0
9
Problem 2.5

• When a system is taken from a to b state along
  acb 80 joules of heat flows into the system and
  the system does 30 joules of work.
• How much heat flows into the system along path
  adb, if the work done by the systems is 10
  joules.
• When the system is returned from b to a along the
  curved path the work done on the system is 20
  joules. Does the system absorb or liberate the
  heat? How much?
• If Ea 0 and Ed 40 joules, find the heat
  absorbed in process ad and db.

c
b

• Answers
• Qadb 60 joules.
• Qba - 70 joules joules (liberate heat) of the
  heat
• Qad 50 J, Qdb 10 J

a
d
10
Problem 2.6
A vessel of volume VB contains n moles of gas at
high pressure. Connected to the vessel is a
capillary tube trough which the gas may slowly
leak out into the atmosphere, where PP0.
Surrounding the vessel and capillary is a water
bath, in which is immersed an electric resistor.
The gas is allowed to leak slowly trough the
capillary into the atmosphere while, at the same
time, electrical energy is dissipated in the
resistor at such a rate that the temperature of
the gas, the vessel, the capillary and the water
is kept equal to that of the surrounding air.
Show that, after as much gas is leaked as is
possible during time ?, the change of internal
energy is where, v0 molar volume of gas at
PP0, ? potential on the resistor, and i is
the current.
11
Problem 2.8
The tension force in a wire is increased quasi
statically and isothermally from ?1 to ?2. If the
length, cross-sectional area and isothermal
Youngs modulus (Y) remain practically constant,
show that the work done by the wire is