A copper calorimeter of mass 100 g contains a lump of ice at 4^ C… - Vidyadip

Question

A copper calorimeter of mass 100 g contains a lump of ice at $4^{\circ} C$. When 520 calories of heat are given to the calorimeter and its contents, the temperature rises from $-4^{\circ} C$ to $-2^{\circ} C$. The addition of another 41540 calories of heat brings the temperature of the calorimeter and its contents to $2^{\circ} C$. Determine the specific heat capacity of copper and the mass of ice present in the calorimeter. Given: Latent heat of fusion of ice $=80 cal / g ^{-1}$ Specific heat capacity of ice $=0.5 cal / g ^{-1}\left({ }^{\circ} C \right)^{-1}$

✓

Answer

Let $s$ be the specific heat capacity of copper and $m$ the mass of ice present in the calorimeter.
We then have, $100 \times s \times[-2-(-4)]+ m \times 0.5 \times[-2-(-4)]=520$ or $200 s+ m =520 \ldots .$. (i)
Also $100 s \times 2-(-2)+ m \times 0.5 \times(-2)+ m \times 80+ m \times 1 \times(2-0)=41540 \ldots . .$. (ii) or $400 s+83 m=41540$
Splving eqn. (i) and (ii),
we get, $m =500 g$ and $s =0.1 cal / g ^{-1}\left({ }^{\circ} C \right)^{-1}$.

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