2494

24-20 M E C HAN I CAL ENG I NEE R I N G REF ERE N C E MAN U A L

39 SPECIFIC HEATS OF REAL GASES D cp =A+BT+CT2 + VT

By definition the specific heat of an ideal gas is indeshyCv cp R lSI] 2495(a)pendent of temperature However the specific heat of

a real gas varies with temperature and (slightly) with pressure There are several ways to find the specific heat of a gas at different temperatures tables graphs and correlationsl4 Table 221 is a typical tabulation of specific heats versus temperature

Equation 2494 is a typical temperature correlation The variation with pressure being small at low presshysures is disregarded The coefficients A B C and D will depend on the units the temperature range over which the correlation is to be used and the desired acshycuracy Typical coefficients are given in Table 249

Cv = cp ~ -- [US] 2495(b)~ K-laquo- 1( I - ~1ep (-r) (tLS) Zl Ct PRACTICE PROBLEMS

1 What is the molar enthalpy of 250degF (120degC) steam with a quality of 92

(A) 16000 Btulbmole (37 MJkmol) (B) 18000 Btulbmole (41 MJkmol) (C) 20000 Btulbmole (46 MJkmol) (D) 22000 Btulbmole (51 MJkmol)

The answer is (C)

gas K A B C D to air 400 to 1200

1200 to 4000 220 to 670 670 to 2220

02405 02459

-1186 X 10-5

322 x10- 5 201 X

-374 X

10-9

10-9 o

-0833

400 to 1000 1000 to 4000

220 to 560 560 to 2220

0453 1152

062 x10-5

3258 x10- 5 2688 X

-4129 X

10-9

10-9 o

-2242

CO 400 to 1200 1200 to 4000

220 to 670 670 to 2220

02534 02763

-235 x10-5

304 x10-5 2688 X

-389 X

10-9

10-9 o

-15

400 to 4000 220 to 2220 0328 32 x10- 5 -44 X 10-9 -333

400 to 1000 1000 to 2500 2500 to 4000

220 to 560 560 to 1390

1390 to 2220

2853 3447 2841

145 x10-5

-47 x10-5

45 x10- 5

-883 X

703 X

-312 X

10-9

10-9

10-9

o o o

400 to 1800 1800 to 4000

220 to 1000 1000 to 2220

04267 03275

2425 x10-5

1467 x10- 5 2385 X

-1359 X

10-9

10-9 o o

400 to 1200 1200 to 4000

220 to 670 670 to 2220

02510 02192

-163 x10-5

438 x 10-5 204 X

-514 X

10-9

10-9 o

-0124

400 to 1200 1200 to 4000

220 to 670 670 to 2220

0213 0340

0188 x10-5

-036 x10-5 203 X

0616 X

10-9

10-9 o

-319

aMultiply values in this table by 2326 to obtain coefficients for specific heats in kJkgmiddotK Adapted from a table published in Engineering Thermodynamics C O Mackay W N Barnard and F O Ellenwood (John Wiley New York 1957)

14It is also possible to calculate the specific heat over a small temperature range if the enthalpies are known (eg from an air table) from Cp = tlh tlT However if the enthalpies are known it is unlikely that the specific heat will be needed

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THE R MOD Y N A M I CPR 0 PER TIE S 0 F SUB S TAN C E S 24-21

2 What is the ratio of specific heats for air at 600degF (300degC)7

(A) 133 (B) 138 (C) 141 (D) 167

The answer is (B)

3 What is the density of helium at 600degF (300degC) and one standard atmosphere

(A) 00052 Ibmft3 (0085 kgm3)

(B) 00061 Ibmft3 (0098 kgm3 )

(C) 00076 Ibmft3 (012 kgm3 )

(D) 00095 Ibmft3 (015 kgm3 )

The answer is (A)

~~v1-e ~ peamptYG

LA r~ ~SIV2M-)4gtleiG l 12 ( l3cu JP6~y prshy1~

== ~etOyfT LshyAc--shy

OJ IlO~l1~ ltgt

o

t Cgt

ke-y- r~Ao ~I a 1~( amp1-1 J-ervlts (JJf r1-s C fewllC tu--eJj

C f (-n or cr dUA-lt7 d-b nv vA~I

C-v -c C -- (VmiddotSmiddot1 Zltfq5(~)C l-U-e 11 y

Leshy a =1f (i)

1 Cf (2- ) V- ----ov~d

CJ ~ c( ~ vufv ect7S(6)

ltuhsp4k efil- ~A (Jl-1 lt r middotmiddot 8ZLd 1gtC helveeuro middot )c-u c1 ~ ~ 24 0 ~C6)

CfiSf

Cv ~ 1 - cPr (3 )

Cf cp

1 c 1- cPa 14)- q(~J

( c )~~ f-u~iYv d tV (-e ampf ~ 2- f9

~ z 1- s6 uLuz -ivr 1t- i ~ 1( t - ~~)lt0

[ lt3(7)) I PROFESSIONAL PUBLICATIONS INC

1. Text1
2. Text4 Cp(T)
3. Joules Constant J Where J = 77817 Lbf-ftBTU