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A block of lead of heat capacity 1 kJ/K is cooled from 200K to 100K in two ways. (a) It is plunged into a large liquid bath at 100K. (b) The block is first cooled to 150K in one liquid bath and then to 100K in another bath. Calculate the entropy changes in the system comprising block plus baths in cooling from 200 K to 100 K in these two cases. Prove that in the limit of an infinite number of intermediate baths the total entropy change is zero.
Ti 90
(^273) 363k M^ O^ 2kg 7 18 273 291k Heat (^) capacity 4200 Jk (^) kg
1 291k
by
5h
dog (^) I MYI entropy F I^ 363K
S MC^ In T^1363 0.2 4,^ in 23 185.75k Q MCFI AT (^) Tf (^) Til F Ti^ SL FCT ly Tang (^) VII
MCDT
AS (^) Bath
M
n
AS
sys DSL DS'b^
AT
100 7 t mygan
a
MCDT Fang^ Ibath I (^) CICIO 4 b 1200 150
(^150) Tang
200T
175k
Tbath
D8 MCAT
100 ΔT^ Tf^ Tif Ti I 1100
MCAT f Targe 502 (^1 ) bath 100
A
System 2 2
I will f
0 C
AS 2.303^ NR^ log^ Y
05
H DU^ Q^ W 5 W
zen
no heat^ exchange reversible (^) process ii sa OF AU^ TAS^
DUCH T
GibbsFunction
DH ΔU^ PΔV^
DG DUT PAV^ UDP^ SDT
constant AT O AU nCuΔT O
DF DU SDT^ O F is constant
iii AH Dut PDU
isothermal (^) process
All O^
DQ 0
AN PDV^ AH^
PDU
for (^) compre ssion^ system Vd^ p
I (^) comy ss^ sys m 11 P tuel^ Δ^
ve
AG AHC^ ve
DUt _S
Ii work^ DIE Wgas nr in^ f isothermally
i 8.314 295
h 16, Wna (^) Pdu due V2^ Tz T (^104) 1.3 10 7m^ 2
104 360 295 el.BY 07m
IA AU
Hence the^ temperature^
is constant during the^ phase^ condition so^
ΔU
remains constant B (^) DH 1 a^ PV
273K 1273 e0 (^) GG cal k m (^5009 80) c 308g 20 E
(^3) f 29k 330.5k m (^) 500g Mz^300 g AS
d
I
CW M^ S
dT CN Mz^
AT
293
Q W KJ 1000J
Q Q E AU M^ UDT FEET a
Dec 1
not
cold (^) I en^1 f
n Cec^ irrev N e Reve Ntec imp
