Three liquids with masses m 1- m 2- m 3 are thoroughly mixed- If their specific heats are C 1- c 2- c 3 and their temperatures are T 1- T 2- T 3 respectively- then the temperature of the mixture is-A- c1 T1-c2 T2-c3 T3-m1 c1-m2 c2-m3 c3B- m1 c1 T1-m2 c2 T2-m3 c3 T3-m1 c1-m2 c2-m3 c3m1 c1-m2 c2-m3 c3C- m1 c1 T1-m2 c2 T2-m3 c3 T3-m1 T1-m2 T2-m3 T3D- m1 T1-m2 T2-m3 T3-c1 T1-c2 T2-c3 T3

You visited us 3 times! Enjoying our articles? Unlock Full Access!

Specific Heat

Three liquids...

Question

Three liquids with masses $m_{1}, m_{2}, m_{3}$ are thoroughly mixed. If their specific heats are $c_{1}, c_{2}, c_{3}$ and their temperatures are $T_{1}, T_{2}, T_{3}$ respectively, then the temperature of the mixture is:

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
Given, $T_{1}, T_{2} a n d T_{3}$ are the temperature of liquids with mass $m_{1}, m_{2} a n d m_{3}$ with specific heats $c_{1}, c_{2} a n d c_{3}$
Let the final temperature be $T^{\circ} C$ .
Total heat supplied by the three liquids in coming down to $0^{\circ} C$ is
$m_{1} c_{1} T_{1} + m_{2} c_{2} T_{2} + m_{3} c_{3} T_{3}$ ......(i)

Total heat used by three liquids in raising temperature from $0^{\circ} C to T^{\circ} C$ is
$m_{1} c_{1} T + m_{2} c_{2} T + m_{3} c_{3} T$ .....(ii)
By equating (i) and (ii) we get,
$m_{1} c_{1} + m_{2} c_{2} + m_{3} c_{3}) T = m_{1} c_{1} T 1 + m_{2} c_{2} T_{2} + m_{3} c_{3} T_{3}$
or, $T = \frac{m_{1} c_{1} T_{1} + m_{2} c_{2} T_{2} + m_{3} c_{3} T_{3}}{m_{1} c_{1} + m_{2} c_{2} + m_{3} c_{3}}$

Suggest Corrections

Similar questions

Three liquids with masses $m_{1}, m_{2}, m_{3}$ are thoroughly mixed, If their specific heats are $c_{1}, c_{2}, c_{3}$ and their temperatures $T_{1}, T_{2}, T_{3}$ respectively, then the temperature of the mixture is

Q. Three liquids with masses

m_{1}, m_{2}, m_{3}

are thoroughly mixed, If their specific heats are

c_{1}, c_{2}, c_{3}

and their temperatures

T_{1}, T_{2}, T_{3}

respectively, then the temperature of the mixture is

Q. Three liquids with masses

m_{1}, m_{2}, m_{3}

are thoroughly mixed, If their specific heats are

c_{1}, c_{2}, c_{3}

and their temperatures

T_{1}, T_{2}, T_{3}

respectively, then the temperature of the mixture is

Q. A calorimeter of mass m contains an equal mass of water in it. The temperature of the water and calorimeter is

t_{2} > 0^{\circ} C

. A block of ice of mass m and temperature

t_{3} < 0^{\circ} C

is gently dropped into the calorimeter. Let

C_{1}, C_{2}

and

C_{3}

be the specific heats of material of calorimeter, water and ice respectively and L be the Latent heat of ice. The whole mixture in the calorimeter becomes ice if

A substance of mass m₁ specific heat capacity C₁ at temperature θ₁ is mixed with another substance of mass m₂ specific heat capacity C₂ at a lower temperature θ₂. Deduce the expression for the temperature θ of mixture.

Join BYJU'S Learning Program

Three liquids with masses m1,m2,m3 are thoroughly mixed. If their specific heats are c1,c2,c3 and their temperatures are T1,T2,T3 respectively, then the temperature of the mixture is:

Three liquids with masses $m_{1}, m_{2}, m_{3}$ are thoroughly mixed. If their specific heats are $c_{1}, c_{2}, c_{3}$ and their temperatures are $T_{1}, T_{2}, T_{3}$ respectively, then the temperature of the mixture is: