Heat Transfer Calorimetry

cpp (Calorimetry & Thermal ElCpansion) 6th March It

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, Cal.II'imetrv,& Thermal EXpa'nSion'~

Cpp

.

..

PART.

';'7,,'1.

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.-.sL I M I'T.E'D'

;:;:::'X;;--

I : SUBJECTIVE. QUESTIONS

Section (A) ,: Calorimetry A 1. ' ,In the following equation calculate the value of H. 1 kg steam at ZOO.C= H + 1 kg water at 100.C (5.- = Constanl = 0.5 Callgm.C) A 2.'

From what heightsh~Uld a piece of ice-(O.C)full so that it melts complelely? Only one-quarter of the energy produced is absorbed by the ice as heat. (Latent heal of ice = 3.4 x l()5J kg-', g.= 10 m/s2)

A 3.

A copper cube of mass 200g slides down on a rough inclined plane of inclination 37. at a constant speed. Assume that any loss in mechanical energy goes into the copper block as thermal energy. Find the increase in the temperalur~ of the block as it slide~ down 60 em. Specific heat capacity of coP,:~:=\20J/kg.K

A 4.

A paddle wheel is connected with a block of mass 10 kg as shown In figure. The wheel is completely immersed in liquid of heat capacity 4000 JIK. The container is adiabatic. For the time interval in which block ~oes down;~t m sloWlycalculate

~,

,if/\ ,,"U/

(-

(',eo,'

(a) Work done on the liquid

'.

-

,

t

\ ,::..,.A

,.'

(b) Heat supplied to the liquid ' ~:,(\", (c) Rise in the temperature of the liquid . ", " \ Neglect the heat capacity of the container and the paddle. (g =10 nillf)

> \ '¥" \ "\ ,';p '_

Seetron (B) : Tlierm&lExpa~SI6~

j~~

.

"

.',.,.

.

B 1.

:"he temp~rature of a m~tal ban!s ~~;Arrange

B 2.

In ascendIng order. ~ '\ A brass disc-fits in a'holein\a steel plate. Would youh'eal or cool the system 10 loosen the disc from the hOle?A-i''nte lh~t\ci. lained rod :~ . ~"W

.

(,

6.

(C1..= 3a

.

0,. were

.,

The volume thermal expansion coefficienl of an ideal gas at conslant pressure is (A)T

(6)1"

1

(D) T2

.

(Here T = absolute lemperalure of gas) 7.

.

,

A metal banimmersed in water weighs w, aIS"C and w. at SO"C.The coefficiento~cubical expansion of metal is less than that of water. Then (AI w, > w, (B) w, < w. (Cl w, = w. (D) dala is insufficient ..'

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4

More th'an one choice type 8.

When two nonreactive samples atdiffe~nttemperatures are mixed In an isolated'containerotnegligible heat capacity the temperature of the mixture can be: .' . . (A) lesser than lower or greater than higher temperature' (8) equal to fower or higher temperature (Cl greater than lower but lesser than higher temperature (D) average of lower and higher temperatures

9._

There is a rectangular metal plate in which two cavities in the shape of rectangle and circle are made, as shown with dimensions. P and are the centres of these cavities. On healing the plate, which of the foliowing quantities increase?

a

f

(A) nr. 2,

+0p

(8) ab

Column II (A) volume of cylinder inside the liquid remains constant '\:,.• .

(PlY = 0

(B) volume of cylinder outside the liquid remains constant .

(q)y

(C) Height of cylinder outside the liquid remairlS constant .'

.

(rly= 3a

(0) Height of cylinder irlSide the liquid remain constant

(s)y

--

= 2a

pd

=. ( 2a + a -pd )

In the following question column - I represents some physical quantities & column-ll represents their units, match them (A) (B) (C) (D)

Column I . Coefficient of linear expansion Water equivalent heat capacity Specific heat

(p) (q) (r)

Column II CaIrC gm (OCr'

(5)

CaUgOC

.,

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5

PART ~ \I : COMPREHENSION Comprehension #1 A 0.60 kg sample of water and a sample of ice are placed in two compartments , separated by a conducting wall, i,na thermally insulated container. The rate of heat water to the ice though the conducting wall is constant p. until thermal equilibrium temperature T of the liquid water and the ice are given in graph as functions of time the compartments remain homogeneous during whole heat transfer process. Given specific heat of ice = 2100 jlkg-K Given specific heat of water = 4200 J/kg-K Latent heat of fusion of fce = 3.3 x 10s J/kg

. . ------•••• B', ------..• .Ice.... -.water---- ----...... '.•• -- .. ' -----~-

" A and B that are transfer from the is reached. The l. Temperature of

20

'

-------f'Z. •••.••• ~ .•.• ,,'

______

conducting

,t

.•

.••.•.••Insulating wali

-20

3.

Th'~I~~rn":4 ,:~J~;~ ~

4.

The initial mnss oHhe ICe In.thecontalner

(A) 42.0 W (A) 0.36 ~

-"'. (B).~6'~""fi

\

(~( 1.2 kg

\.

(C)

IS equal to,

'~~I!\

Q;.:t \~ .. 5.

'

(Cl'2,:i11.:4253355 4253-155 1

15

9.

At = 1.91.mm = At, + At. =:> 0.191 em t,a, Ae + t,a, Ae. =:) 0.191 = (30 ~ 17 ~ 10'" + 70 a,) ~ 100. a. = 2 ~ 10..0

=

Y=

F

-;:;;xe

F,

= F.

Y,Aa,Ae;= Y.Aa. Ae.

Y,a, 1.3x10" x1.7~10-s ------= 1.105 x 10"N/m' Y :.• = ~ = 2x10-5 10.

Wo = mg = 46 9 wI alO = 27. C W, = 30 gm wt = Wo- B, alO 42.'C W. = 30.5 9 wt = Wo- B.

,

•=

B.

..

~

B, = (46 - 30)gm =:>

15.5 .

V,P2

= V1P1

S,

= 15.5 gm wt = V. P,9

16 = (1 + 3a,

~

-

12 ~ 15) ~ 1.24

_ fl(15.5 ~ 1.24)_1lx~ a, - ~ 16 1.2 45

J

11.

---t,--I

I

12.

aUI .•C. If

\ c:•

i/JI

.,\.

rOcls are free to expand.

---1--+

!Illffili

t, = to (1 + a,O) t. = to (1 + a,O) F/A y= xlt

Fxi

x=. AY

2Fx to AY

•

Fxto AY

•

"';

if a,>~, +a,AO)-i

..... (i)

= i-io (1 + a,AO)

....:(ii)

. =io(l

a'•

by solving (i) and (ii) wege!

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16

3.

both discs are in series combination

R=R,+R, _PF_t_+F Pc Ie = ~p~Fl_1_+_U~F_T]t~F + ,-P",e,-11_+_u~c~T)~t~e A A A' 'f"""" A. '" Peue -=--te . PFuF HF He 114.

PFIF

= Pele

=45

.

3 = 20

(a)

i = 1 { 1 + 2 x 10 -5 x20}

(b)

l:010{1-4x

(c)

t= 10{ 1 +4x10-4}

(el)

% it = - 4

X

10-4)

10-2 %

.

-4x10-2 %l2= 1+4x10-4 %;: -4x 10-2% (e) ..

In the figureh, 52.8 em, .h2 51 em and h = 49 em Now pressure at B = pressure at Therefore .•

=

=

c.

p. + h, Pw g • h PS' g = Po + h2 PS' 9 -.h PRS' g

==-

.

PRS' (h, + h )

= PS' (h2 + h) PO'"

(1+.95r)

~

h2 +h'

=' h,+h

(1+5'() .

==-

1+5y _ 51+49 .100 1+95'1 - 52.8+49 = 101.8

Solving Ihis equation, we gel .\ r= 2 x 10'" per "C.

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17

CPP (Heat Transfer) 6th March 11

, HealTranS'er.

cpp~

Exercise: #1 . .. .

.

Section (A) : Thermal conduction In linear conductors at steady state A 1. A uniform slab ofdimension 1Oem x 10em x 1em is kept be.tweentwo Iie ..

14•... Airietalblock of heat capacity 90 JiC placed in a rOOl!)at 25'C Is heated eleCtrically. The heater Is switched ", .','offwhenlhe temperature reaches 35~G.The temperature of the block rises at the rate of2'C/s'justaflerthe " .•heater-is'switched on and falls althe rate of 0.2 'Cis just after the healeris switched off. Assume Newton's .. law.of cooling ~ hold. (a) Find the power of the heater. (b) Find the power radiated by the block just after the heater Is switched off. (c) Find the power radiated by the block when the temperatUre of the block is 30.C. (d) Assuming that the power radiated at 30'C respresents the average value in the heating process, find the time for which the heater Was kflpton. .'

~Wi1t.il»lt!gmmiQDm_1II choice At. ..) Single

1.

type

."

Two identical square rods of metal are welded end to end as shown in figure (a), Assume that 10 cal of heat flows through the rods in 2 min. Now the rods are welded as shown,in'figure, (b). The'ti~il~ould take for 10 cal to flow through the rods now, is .

.

.

"

O'C ,

.

(A) 0.75 min

2.

6sf' "i..'"

(8) 0~5 mi;

(b)

~

(C) 1.5 min?

.

)

(0) 1 min

~ of. copper, """'" aluminium F, ./ ,v~ 20 cm long and 4 em in diameter, are Three metal rods made and brass, each "\ 'l\.. 't'~ ~ or-. placed end to end with aluminium between the other, two. Tne free ends of copper and brass are maintaine A. (il) ey < ex' Ay< Ax

(C)

By

> ex; Ay Ax ~. Woodennd .

Oil out . .

. '~.Oil

..V. I •... '*)7 ...

(i)

the radiation loss (in Js-' nr') fromlhe lid and.'

(ii)

the temperatureT (in ~C)of the 011. ThE!thenna..1,ciondUcliv~a.n.•,d..e..,m .•.•.•.. iSS .... ivily OfWOO~d;~. ~~~ •...•• ' 'of,.' 0.149 Wm-1 K-I and 0.6 respeclivelv, The va.IUS'.of the Stefan's co..nstari.'.!l. 'fl\•,';;", ifi;. ", 1

0= ~

~ 10-"

...•

~

r(\

'~

Wnr'K"(N~lectheatlos~;'Conyectiori~g:~~'~~YI€:~correctto

.

\

"i

•

:3~

(A)2. ~....... "~(B~t 2 "',' (C)4 . 1 .(0) 1.4 '.' .' Three disCs same ma.terialA; B, C of radii2chi, 4 em and 6 em respeCtively are Coated with carbOnblack .

of

10.

r~~.~::r: .. e.:,.~.~~'",£m"' ••••_,"'""'~"'.~:',':~ (':i(t~ ':'(:\(BY~'. ;.:'.;

:

..)

co.:I.I.~ .•

(C)~ .... .' 11,"" One end of a rod ()f lenQth L and cross-sectional area A IS kept In a furnace :~.()fl{mpelature TI.Jhe other end of the rod Is kept at a iemperature T•. the .

~

12.

.

. . the neareslwhole numberl~ •. \~ ~~\ . .' . ~ ..... Two containers, one is having '"ice at O'C ana other containing g waler at100'C are connected by two . . .. T,). The rate of heat transfer through Ihe Sla~.;' \ \ ~

5.

olthe '

4

,;e

.,_,0.. "~T:>'--~:r~ -'A.\it

(A(T - T )1