$80$ g of water at $60^{o}$ C is poured into a vessel containing $100$ of water at $20^{o}$ C. The final temperature recorded is $30^{o}$ C. Calculate thermal capacity of vessel.

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Solution

Heat lost by water to change it is temperature from $60 ℃$ to $30 ℃ = m s △$ T.
$= 40 \times 4.2 \times 30$
$= 5040 J .$
Heat gained by water,
$= 50 \times 4.2 \times 10$
$= 2100 J .$
Heat gained by vessel,
$=$ Heat capacity $\times$ 10
Heat lost by hot water,
$=$ heat lost by cold water + heat gained by vessel.
$∴$ Heat gained by vessel,
$= 5040 - 2100$
$= 2940.$
Heat capacity $\times 10 = 2940$
Heat capacity $= 2940 / 10$
$= 294 J / ℃$

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