Question

A body of mass "m1" of a substance of specific heat capacity cl , at a temperature t1 is mixed with another body of mass "m2" of specific heat capacity "c2" at a lower temperature t2. Deduce an expression for the temperature of the mixture t3.

Answer 1

Answer:

The required expression of the temperature of mixture t₃ will be :-

  t ₃ =  $\dfrac{m_{1} c_{1}t_{1} + m_{2}c_{2}t_{2}}{m_{1}c_{1} + m_{2}c_{2} }$.

Explanation:

Heat evolved or absorbed after a change in temprature is given by:-

ΔQ = mcΔT

   where m = mass of substance

               c = specific heat capacity of the substance

               ΔT = Change in temperature.

Now, if the vesel is isolated, then total change in heat must be zero,i.e,

ΔQ = 0.

or,   m₁c₁Δt₁  +  m₂c₂Δt₂ = 0

or,   m₁c₁(t₃-t₁) +  m₂c₂(t₃-t₂) = 0

or,   m₁c₁t₃ -m₁c₁t₁ + m₂c₂t₃ - m₂c₂t₂ = 0

or,   (m₁c₁ + m₂c₂)t₃ = m₁c₁t₁ + m₂c₂t₂

or,   t ₃ =  $\dfrac{m_{1} c_{1}t_{1} + m_{2}c_{2}t_{2}}{m_{1}c_{1} + m_{2}c_{2} }$