Question 571: Thermodynamics & KTG

Question

Three containers C
1
, C
2
and C
3
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 ..........
![](https://imagex.cdn.examgoal.net/7k9k2k5hhzgna/7354923f-638e-45c4-ab36-7152f0772a3f/91a06a60-38ca-11ea-92dd-4b9c3519996f/file-7k9k2k5hhzgnb-323w.jpg)

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

Integer / Numeric Answer Type