It's getting too cold!

Classical Mechanics Level 3

500 g 500\text{ g} of a metal of specific heat capacity 0.25 Jg − 1 ∘ C − 1 0.25 \text{ Jg}^{-1}\ ^\circ\text{C}^{-1} at 125 ∘ C 125\ ^\circ\text{C} is added to an equal amount of ice at 0 ∘ C 0\ ^\circ\text{C} . Did all the ice melt?

If so, enter 555.

If not, enter the quantity of unmelted ice in grams (up to 2 decimal places).

Note: Specific latent heat of ice = 336 Jg − 1 . 336\text{ Jg}^{-1}.


The answer is 453.49.

Ashish Menon by Ashish Menon , 20, India

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1 solution

Ashish Menon
Apr 7, 2016

Relevant wiki: Heat Transfer

Heat energy given out by metal = m × c × θ F = 500 × 0.25 × 125 = 15625 J Heat energy absorbed by ice = m × L = 500 × 336 = 168000 J \begin{aligned} \text{Heat energy given out by metal} & = m × c × {\theta}_F\\ & = 500 × 0.25 × 125\\ & = 15625J\\ \\ \text{Heat energy absorbed by ice} & = m × L\\ & = 500 × 336\\ & = 168000J \end{aligned} Clearly, this is way higher than the heat energy given out by the metal. So, it is proved that all ice does not melt.
Let x be the amount of ice melted by the heat given out by metal.
⟹ 15625 = x × 336 ⟹ x = 46.502 g So, the amount of unmelted ice = ( 500 − 46.502 ) g ≈ 453.49 g \begin{aligned} \implies 15625 &= x × 336\\ \implies x & = 46.502g\\ \\ \text{So, the amount of unmelted ice} & = (500 - 46.502)g\\ & \approx \boxed{453.49g} \end{aligned}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

The unit of latent heat is J/gm not J/gm-C

Aniket Sanghi - 5 years, 2 months ago

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