Special BLOG # 1: Saturday review section

1st.....this is the practice exam....

http://docs.google.com/View?docid=dhtfdzv3_1f9x8jgjp

getting into subject...

Chapter 17

Thermal expansion and thermal stress

delta means changing

Linear expansion(1D):

delta L = alpha * Lo * delta T
@where L is length, Lo is the initial length and T for temperture


Volume(3D):

delta V = beta * Vo * delta T
@where V is volume, Vo is the initial volume and T for temperture

(there's also a equation for 2D....just change the V or L to A(area) and multiply alpha by 2)

here's the alpha and beta from the book....









Thermal conductivity

Q = (k*A*delta T) / L
@ where k = specific Heat, A = cross-section Area, T= temperture, L = length

so...how does this work...

since Q1 = Q2 (if, they conduct together)

so we can set up like....(taking Copper & Aluminum as example.....)

QCu = QAl

then, [400*A*(Tf - To)]/LCu = [240*A*(Tf - To)]/LAl

then we can find the common variable Tf

Phase Change

Temperature remains CONSTANT until change of phase is complete .remember this....very important....

Lf = Heat of Fusion

Lf => 80(cal/gram) = 3.35 x 10^5 (J/kg)

Lv= Heat of Evaoiration

Lv=> 540(cal/gram) = 2.26 x 10^6 (J/kg)

and remember!!!!!! Qgain + Qlost =0

example is in here....http://physics4b.blogspot.com/2008/09/third-daysighlong-weekend-no-more.html

Chapter 18

Ideal Gas Law

PV = nrT
for P=pressure(pa), V=vloume(m^3), n=# of moles(mol), r = 8.3145 , T=temperture

or

PV = NkBT
for P=pressure(pa), V=vloume(m^3), N=# of Atoms, kB = 1.38x 10^-23 , T=temperture

they are same equation....only different is dealing with mol or atom....differ by an Avocado's number....(i know...just think it as a typo)

oh......by the way.... 1 atm = 1.01 x 10^5 Pa....always convert it to Pa

Vrms = sqrt( [3*kB*T]/m )
@ where sqrt() = square root, kB = 1.38 * 10^-23, m = mass of gas(element) atom

or

Vrms = sqrt( [3*R*T]/M )
@ where sqrt() = square root, R= 8.314, M = molar mass of the gas(element)

Ktr = (3/2)*n*R*T

Heat Capacities

Cv = (3/2) * R (monatomic gas )

Cv = (5/2)* R (diatomis gas )

Cv = 3R (monatomic solid)


Chapter 19 & 20

General equation for all

Ein = Q - W

Ein = internal energy, Q=heat, W=work

isochoric

V = const

since there is no changing Volume, there W= P * delta V will just simply equal to 0.

and then the general will be:

Ein = (m*Cv* delta T ) - 0

therefore,

Ein = (m*Cv* delta T )

and we can use this equation for all thermodynamic process, as long as it's Ideal Gas.

(cuz Ein will not change...so this equation will apply everywhere)

isobaric

P = const

since P =const, there is both Q and W.

Q = m*Cp*delta T

W = P * delta V

apply them back to the general equation

Ein = Q - W ,we will get

Ein = m*Cp*delta T - P * delta V

furthermore, apply the Ein we got in the previous part we will get

(m*Cv* delta T ) = (m*Cp*delta T) - (P * delta V)

by this we can calculate everything......for isobaric

isothermal

T = const

since Ein = 0 , therefore

Q + W = 0

(reason why I dont do Q = W is because there will be a sign problem. is you do Q + W , then since one is positive and the other one is negative. we dont have to worry about sign. )

and W in isothermal is

Q = W = nRT * ln Vf / Vo

= P1V1 * ln Vf / Vo

Adiabatic

it means no heat

so, Ein = -W

W = n*Cv*(To -Tf) Note: yes, it's To - Tf(since it can be both release or absorb heat....well..u know what i'm trying to say...)

and for adiabatic....there's something more than this equation... sometimes we need to find P, or V, or T ourself.....in that case....we need to use these equations....

T1V1^(gamma - 1) = T2V2^(gamma-1)

P1V1^(gamma) = T2V2^(gamma)

Buoyang force

1st, buoyang force is a upward force that particle will excert by fluid(or gas).

cutting into subject, the hot balloon. we can simply draw a force diagram.

| FB

|

B

|

| mg

in which FB is the buoyang force upward, and mg is the weight downward.

in the general difinition, B= D * V* g .

B=buoyang force, D=density, V=volume and g = gravity

F = P/A, which also tells that P = FA. P=pressure, F=force, A=area

then we can get the presure excert by buoyang force is simply P = D*g*h (since V/A = height...)

so for the hot balloon, for it to float(upward force = downward force), the force FB = mg. then we can derive many more equation and so on....

oh...remember buoyang force is everywhere!!! even for the bottom of the hot balloon.

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