Question 626: Thermodynamics & KTG

Question

Three containers C1, C2 and C3 have water at
different temperatures. The table below shows
the final temperature T when different amounts
of water (given in litres) are taken from each
containers and mixed (assume no loss of heat
during the process)

The value of $$	heta $$ (in °C to the nearest integer) is ..........

Accepted Answer

Let containers C
1
, C
2
, C
3
contain water at T
1
, T
2
and T
3
temperatures respectively.
Applying law of
calorimetry
1(T
1
Ã¢ÂÂ 60) + 2(T
2
Ã¢ÂÂ 60) = 0
$$ \Rightarrow $$ T
1
+ 2T
2
= 180 ....(1)
1(T
2
Ã¢ÂÂ 30) + 2(T
3
Ã¢ÂÂ 30) = 0
$$ \Rightarrow $$ T
2
+ 2T
3
= 90 ......(2)
2(T
1
Ã¢ÂÂ 60) + 1(T
3
Ã¢ÂÂ 60) = 0
$$ \Rightarrow $$ 2T
1
+ T
3
= 180  .....(3)
from (1), (2), (3)
T
1
= 80
o
C
T
2
= 50
o
C
T
3
= 20
o
C
1 ÃÂ (T
1
Ã¢ÂÂ $$	heta $$) + 1 ÃÂ(T
2
Ã¢ÂÂ $$	heta $$) + 1(T
3
Ã¢ÂÂ $$	heta $$) = 0
$$ \Rightarrow $$ T
1
+ T
2
+ T
3
= 3$$	heta $$
$$ \Rightarrow $$ $$	heta $$ = $${{80 + 50 + 20} \over 3}$$ = 50
o
C

Thermodynamics & KTG

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