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A 35 g sample of Fe is dropped into 80 g of water at 20 degrees Celsius. What is the final...

Question:

A 35 g sample of Fe is dropped into 80 g of water at 20 degrees Celsius. What is the final (equilibrium) temperature of the iron/water?

Conservation of Energy:

  • Assuming a hot object at initial temperature ({eq}\textrm{T}_{1} {/eq}) is brought in contact with another object at a temperature {eq}\textrm{T}_{2} {/eq} such that {eq}\textrm{T}_{2} {/eq}<{eq}\textrm{T}_{1} {/eq}.
  • Both bodies will attain a common temperature after some time as heat lost by the first object will be equal to the heat gained by another object. Energy is always conserved during any process.

Answer and Explanation:

Given,

  • Amount of water = m = 80 g
  • Initial temperature of water = {eq}\textrm{T}_{1} {/eq} = {eq}20^{\circ}C {/eq}
  • Specific heat capacity of water = c = 4.184 {eq}\textrm{J/g}^{\circ}C {/eq}
  • Specific heat capacity of Fe = c' = 0.450 {eq}\textrm{J/g}^{\circ}C {/eq}
  • Amount of Fe = m' = 35 g
  • Assuming initial temperature of iron ({eq}\textrm{T}_{2} {/eq}) = {eq}60^{\circ}C {/eq}
  • Suppose the final temperature of the solution be {eq}\textrm{T}_{f} {/eq}

Heat lost by Fe = Heat gained by water

{eq}\begin{align*} \textrm{mc}\left ( 60-\textrm{T}_{f} \right )^{\circ}C&=m'c'\left ( T_{f}-20 \right )^{\circ}C \\ 35 \textrm{ g}\times 0.450 \textrm{ J/g}^{\circ}C\times \left ( 60-\textrm{T}_{f} \right )^{\circ}C&=80\textrm{ g}\times 4.184 \textrm{ J/g}^{\circ}C\times \left ( T_{f}-20 \right )^{\circ}C \\ \textrm{T}_{f}&=21.79^{\circ}C \end{align*} \\ \boxed{\textrm{Final temperature of solution} = 21.79^{\circ}C} {/eq}


Learn more about this topic:

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What is Energy Conservation? - Definition, Process & Examples

from ICSE Environmental Science: Study Guide & Syllabus

Chapter 1 / Lesson 6
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