Engg1050 First Law 2007

ENGG1050 Engineering Thermodynamics First Law of Thermodynamics

ENGG1050 Engineering Thermodynamics

Work (read C&B 4-1) f

• Mech Mechan anic ical al Work Work :

∫

W = F .ds i

• Kineti Kineticc Energy: Energy: work work done done by force force on movi moving ng body (assume F in direction of motion) motion)

dW = ma.ds = m

du dt

.u.dt = mu.du

u =v

KE =

∫

mu.du = 0.5mv 2

u =0 ENGG1050 Engineering Thermodynamics

1

Work • Gravitational Potential Energy PE=mgh • Moving Boundary Work (e.g. piston) dW = F .ds = PA.ds = P.dV 2

2

∫

∫

1

1

W12 = P (V ).dV = m P (v ).dv • Work done depends on path as well as start/end states (area under P vs V curve).


Other forms of Work • Electrical: W = VI∆t • Shaft Work: W = 2πnT = 2πnr×F • Spring Work: W = 0.5k(x 22-x12) • Generalised Work Form of Work

Gen. Force

Gen. Displacement

Electrical

Voltage

Charge

Magnetic

Mag. Field Strength

Mag. Dipole Moment

Elec. Polarisation

Elec. Field Strength

Polarization of Medium


2

Work example 4-8. A mass of 5kg of saturated water vapor at 300kPa is heated at constant pressure until the temperature reaches 200°C. Calculate the work done by the steam during this process.


First Law – Closed Systems (read C&B 4-2)

• Energy is Conserved • Definitions – Adiabatic:

process in which there is no heat transfer

– Isothermal:

constant temperature

– Isobaric:

constant pressure

– Isochoric:

constant (specific) volume

– Isentropic:

constant entropy

– Isenthalpic:

constant enthalpy


3

Internal energy •

Internal energy, U , a property

•

As a property, can be determined from two other properties:

•

Also has an intensive form, specific internal energy:

Can also obtain U from charts or tables ENGG1050 Engineering Thermodynamics

Definition of heat •

Consider a process in which there is heat transfer, i.e., it is not adiabatic

Often referred to as the First Law

Q depends on path

W depends on path

But ΔE is path-independent ENGG1050 Engineering Thermodynamics

4

Heat & Work - Conventions • Signs:

Heat transfer to a system + Work done by a system

+

Heat transfer from a system Work done on a system

-


Heat & Work - Similarities • Both are boundary phenomena • Systems possess internal energy, but not heat or work • Both are associated with a process, NOT a state. • Both are functions of path, not just initial and final states


5

First Law examples 4-35. A piston-cylinder device contains steam initially at 1MPa, 450°C, and 2.5m 3. Steam is allowed to cool at constant pressure until it first starts condensing. Show the process on a T-v diagram with respect to saturation lines and determine (a) the mass of the steam, (b) the final temperature. And (c) the amount of heat transfer.


Specific Heats (read C&B 4-3 & 4-4)

• Energy required to raise the temperature of a unit mass of a substance by one degree. • cv for process at constant (specific) volume • c p for process at constant pressure 2

Δu = ∫ cv (T )dT 1 2

Δh = ∫ cP (T )dT 1 ENGG1050 Engineering Thermodynamics

6

Ideal Gas Specific Heat • c p=cv + R

(Why?)

• How are c p and cv related for solids & liquids? • Air in a piston-cylinder device is heated at constant pressure (1 atmosphere) from 25°C to 100°C. What is the change in internal energy per kilogram of air?


Enthalpy (read C&B 4-4 & 4-5)

• New extensive property: H = U + PV • Specific Enthalpy: h = u + Pv • Particularly useful for characterising flows (open systems). E.G. (specific) energy of flowing fluid:

θ =

Pv + u + ke + pe = h + ke + pe


7

Enthalpy examples 1. What is the change in enthalpy of 1kg of steam from state 1 to state 2 (get values)? How does this compare with the change in internal energy? 2. A fluid flows through a turbine at a rate of 5kg/s. At the turbine output, the specific enthalpy of the fluid has dropped from its input value by 50kJ/kg. What is the power output from this turbine?


First Law – Gas Processes (read these notes)

• Joule Experiment: For ideal gas, U only depends on T (not P, V) • Isochoric: V1=V2, so P1/T1 = P2/T2 • Isobaric: P1=P2, so V1/T1=V2/T2 • Isothermal: T1=T2, so P1V1=P2V2


8

Isothermal Ideal Gas Process: Work and Heat • ∆u = 0

(T constant)

• ∆h = ∆u + ∆Pv = 0

(Pv constant)

v2

q=w=

∫

v2

P(v) dv =

v1 v2

= RT ∫ v1

∫

RT

v1

v

dv

⎛v ⎞ ⎛P ⎞ = RT ln ⎜ 2 ⎟ = RT ln ⎜ 1 ⎟ v ⎝ v1 ⎠ ⎝ P2 ⎠

dv


Adiabatic Ideal Gas Processes • Reversible, & assume cv doesn’t vary • Introduce ratio of specific heats k = c p/cv = 1 + R/cv – For monatomic gas, k ≈1.67 – Diatomic gas, k ≈1.4 – Larger molecules, k ≈1.32 (see Table A-2)


9

Adiabatic Processes… du = − Pdv cv dT = − dT T

=−

RT

v R dv

cv v

dv

= −(k − 1)

dv v

⎛ ⎛ v ⎞ k −1 ⎞ ln = ln ⎜ ⎜ 1 ⎟ ⎟ ⎜ ⎝ v2 ⎠ ⎟ T1 ⎝ ⎠ T2


⎛ T2 ⎞ ⎛ v1 ⎞ ⎜ ⎟=⎜ ⎟ ⎝ T1 ⎠ ⎝ v2 ⎠

k −1

⎛ P2 ⎞ ⎛ v1 ⎞ so ⎜ ⎟ = ⎜ ⎟ ⎝ P1 ⎠ ⎝ v2 ⎠

⎛ T2 , but for ideal gas ⎜ ⎝ T1

⎞ ⎛ P2 v2 ⎞ ⎟=⎜ ⎟ Pv ⎠ ⎝ 11⎠

k

or

Pv k = const

k −1 ⎡ ⎤ k RT1 ⎢ ⎛ P2 ⎞ ⎥ 1− ⎜ ⎟ Show that : w = ⎢ k −1 P1 ⎠ ⎥ ⎝ ⎣⎢ ⎦⎥


10

Gas Processes -Examples • In an insulated tank, a diaphragm separates a region of gas from an evacuated region. What happens if the diaphragm ruptures? • A non-porous balloon if inflated with Helium to a volume of 3L at a temperature of 20 °C. Upon exposure to sunlight, its temperature increases to 50°C: Does the volume increase or decrease?


First Law – Open Systems (read C&B 5-1 to 5-3)

• Initially restrict to STEADY FLOW SYSTEMS for ease of analysis • Carefully define the CONTROL VOLUME – Mass Balance (rate of mass inflow equals rate of mass outflow) – Energy Balance (Ėin =Ėout )

• e.g. Analysis of hot water system


11

Open Systems… • In general, to analyse a steady flow system, we need to consider: .

.

 , H ,KE , PE Q , W • For single stream systems

 ( Δh + Δke + Δpe ) Q net − Wnet = m ENGG1050 Engineering Thermodynamics

Open Systems examples • A turbine is driven by input of steam at a rate of 5.50kg/s. The steam loses 30.0kJ/kg on enthalpy as it passes through the turbine. What is the maximum power output of the turbine? • What electrical power input is needed to maintain the hot water temperature while you shower?


12

Steady Flow Engineering Devices (read C&B 5-4)

• Nozzles and Diffusers • Turbines and Compressors • Throttling Valves • Mixing Chambers • Heat Exchangers • Pipes and Ducts


Devices – Examples • C & B questions (5-31, 5-62, 5-78, 5-113): • In what applications are the devices listed on the previous page used?


13

Unsteady Flow Processes (read C&B 5-5)

• Changes within the control volume over time. – Shape/Size of control volume changes – Influx/Efflux of mass

• Mass & Energy Balance similar to steady flow, but net influx/efflux may not be zero. – Analysis often simplified by assuming “uniform flow” over duration of process.

• e.g. Charging LPG cylinder


14

Engg1050 First Law 2007

Recommend Documents