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 liters) are taken from each container a

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 liters) are taken from each container and mixed (assume no loss of heat during the process) C 1 C 2 C 3 T 1 l 2 l - - 60 o C - - 1 l 2 l 30 o C 2 l - - 1 l 60 o C 1 l 1 l 1 l θ The value of θ (in o C to the nearest integer) is___________

TestHub · Accepted Answer

Let θ 1 , θ 2 and θ 3 be the temperatures of water in three containers. 1 θ 1 + 2 θ 2 + 0 θ 3 = 1 + 2 60 θ 1 + 2 θ 2 = 180 …. (1) 0 × θ 1 + 1 × θ 2 + 2 × θ 3 = 1 + 2 30 θ 2 + 2 θ 3 = 90 …… (2) 2 × θ 1 + 0 × θ 2 + 1 × θ 3 = 2 + 1 60 2 θ 1 + θ 3 = 180 …. (3) and θ 1 + θ 2 + θ 3 = 1 + 1 + 1 θ from (1)+(2)+(3) 3 θ 1 + 3 θ 2 + 3 θ 3 = 450 ⟹ θ 1 + θ 2 + θ 3 = 150 from (4) equation 150 = 3 θ ⟹ θ = 50 ° C

$C_{1}$	$C_{2}$	$C_{3}$	$T$
$1 l$	$2 l$	$- -$	$60^{o} C$
$- -$	$1 l$	$2 l$	$30^{o} C$
$2 l$	$- -$	$1 l$	$60^{o} C$
$1 l$	$1 l$	$1 l$	$θ$

Physics - Heat & Thermo Question with Solution | TestHub

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