Thermodynamics OSU w0-w1

week 0 covered, week 1 covered

static principle

A pure substance requires knowledge of 2 independent, intensive properties to define the state (know other properties)

Intensive

independent of mass: T P v

Extensive

depends on mass: u m E V h s

relative temps/pressures

C, F, KPa (gage), KPa (vacuum)

absolute temps/pressures

K, R, KPa

Ideal gas laws (2)

PV = mRT

Pv = RT

In the ideal gas law with R (w line above), what is the equation for R?

R = R^- / M

molarity equation

m = n / M

For KE, PE, and U, which uses KJ and which uses J?

U uses KJ, rest J

isometric

the volume is constant: v1 = v2

isoveric

Pressure is constant: P2 = P1

isothermal

Temperature is constant: T2 = T1

polytropic

p2v2 = p1v1

pv^n is constant

isentropic

s2 = s1

Pressure

P (Pa, bar)

specific volume

v (m^3/Kg)

specific internal energy

u (KJ/Kg)

energy per mass

e (J/Kg)

internal energy

U (KJ)

total energy

E (J)

distance from x

z (m)

total enthalpy

H (J)

specific enthalpy

h (J/kg)

specific entropy

s (Kj/Kg*K)

total entropy

S (KJ/K)

gas property units

R (KJ/Kmol *K)

heat transferred

Q (Btu/hr)

specific heat (all eqs)

c_v = du/dt

cv = u_2 - u_1 integral t1 →t2 c_v dt

c_v = (T2 + T1)/2 (closed systems only)

if a system is closed, assume: 

PE and KE = 0 if no info given

use a cv, cp, c_something value to use

u_2 - u_1 = c_x(T2-T1)

If using the ideal gas equation in a closed system

always assume ideal gas

assumptions for isoveric systems

p2 = p1 and if the system is closed:

m1RT1 / v1 = m2RT2 / v2

T2/T1 = v2/v1

m2 = m1

assumptions about isometric systems

v2 = v1 and if the system is closed:

T2/T1 = P2/P1

m2 = m1

assumptions about isothermal systems

since we know T2 = T1 then:

P1V = mRT1

if closed:

P1/P2 = v2/v1

refrigerants

things that may change phase

phases (7)

1. supercooled or compressed liquid

2. saturated liquid

3. saturated liquid + vapor mixture

4. saturated vapor

5. superheated vapor

6. critical point

specific heat vs. pressure phases plot

1. supercooled or compressed liquid

2. saturated liquid

3. saturated liquid + vapor mixture

4. saturated vapor

5. superheated vapor

6. critical point

specific heat vs. temperature phases plot

1. supercooled or compressed liquid

2. saturated liquid

3. saturated liquid + vapor mixture

4. saturated vapor

5. superheated vapor

6. critical point

quality

x = mg / (mf + mg)

unitless

mg = mass of vapor (kg)

mf = mass of liquid (kg)

quality of a

saturated liquid: ___
saturated vapor: ___

saturated mixture: ___

x=0

x=1

0 < x < 1

finding phases with vf, vg and T_sat given pressure and temperature

when referring to water in this class, what state is it in?

vapor!

If a material is in a saturated state:

temperature and pressure are dependent

so

P = psat@T

or

T = Tsat @P

a material is a subcooled liquid if

T < T_sat @ P

P > P_sat @ 

a material is a superheated vapor if 

T > T_sat @ P

P < Psat @ T

if v > vg, u > ug, h > hg, etc.

the material is a ____

superheated vapor

if v < vf, u < uf, h < hf, etc

the material is a  _____

supercooled liquid

if vf < v < vg

(samr for uu,h,etc)

the material is a _____

saturated mixture

if v = vf the material is a ____

if v = vg the material is a ___

saturated liquid

saturated vapor

for finding properties, the 1st step is to determine the region, What do we do if we determine its a saturated liquid?

use “f”

v = vf, u = uf, h = hf, etc

for finding properties, the 1st step is to determine the region, What do we do if we determine its a saturated vapor?

use “g”

v = vg, etc

for finding properties, the 1st step is to determine the region, What do we do if we determine its a saturated mixture?

use quality: x = xg(xf + xg)

v = (1-x)vf + x*vg

u = (1/x)uf + x^ug

h = (1/x)uf + x^hg

an additional way to write the quality equation using v, vg, and vf

x = (v - vf)/(vg - vf)

If you have T, use list ___

if you have P, use list ___

A-2

A-3

if a material is a superheated vapor, that means (T,P)

T > Tsat @P

P < Tsat @T

if a material is a supercooled liquid

use A-5 if P > 2.5 MPa

use A-2 if P <= 2.5 MPa

and assume u = uf @T, v = vf @T

change in energy equation for a closed system

E_2 - E_1 = Q-W

Q is positive when it ____ the system

Q is negative when it ____ the system

enters

leaves

work equation for this class

W = S *integral(V1,V2) Pdv

work per mass

w = W/m = integral(w1,w1) Pdv

for isoveric processes with work

P2 = P1

W = P * integral(v1,v2)dV = P(V2-V1)

for isoveric processes

v2 = v1

W_b = 0

W_b = work done on the boundary

dealing with ideal gases

for isoveric situations:

W = P2V2 - P1V1 = m2RT2 - m1RTv

dealing with ideal gases

for isothermal processes:

m2RT2 = P2v2 = m1RT1 = P1V1

P1V1ln(V2/V1) = mRT1ln(V2/V1)