Question

equal masses of three liquids A B and C have temperature 10 degree celsius ,25 degree Celsius and 40 degree Celsius respectively. if A and B are mixed the mixture has a temperature of 15 degree Celsius and if B and C are mixed the mixture has a temperature of 30 degree Celsius if A and C are mixed then the mixture will have the temperature of what




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Answer 1

The temperature of the mixture is 16°C

Given:

Temperature of liquid A = 10°C

Temperature of liquid B = 25°C

Temperature of liquid C = 40°C

To find:

Temperature of the mixture when A and C are mixed = ?

Formula used:

Heat added is given by the formula:

$\bold{Q=mc \Delta T}$

Where,

m = Mass

c = Specific heat

$\bold{\Delta T}$ = Change in temperature

Solution:

Let the specific heat of the liquid A, B, and C be a, b, and c.

Let the mass of the liquids be m.

Now, the heat added when ‘A’ and ‘B’ is mixed:

$\bold{ma(15-10)=mb(25-15)}$

$\bold{\Rightarrow 5ma=10mb}$

$\bold{\Rightarrow a=2b\longrightarrow (1)}$

Now, the heat added when ‘B’ and ‘C’ is mixed:

$\bold{mb(30-25)=mc(40-30)}$

$\bold{\Rightarrow 5mb=10mc}$

$\bold{\Rightarrow b=2c\longrightarrow (2)}$

Now, equation (1) and (2) becomes,

$\bold{a=2b=4c\longrightarrow (3)}$

Let x be the temperature when liquid ‘A’ and ‘C’ are mixed.

$\bold{ma(x-10)=mc(40-x)}$

$\bold{\frac{a}{c}=\frac{40-x}{x-10}}$

From equation (3)

$\bold{\frac{4}{1}=\frac{40-x}{x-10}}$

$\bold{4x-40=40-x}$

$\bold{4x+x=40+40}$

$\bold{5x=80}$

$\bold{\therefore x=16\° C}$