3. A 31.2-g piece of silver (s = 0.237 J/(g · °C)), initially at 277.2°C, is added to 185.8 g of a liquid, initially at 24.4°C, in an insulated container. The final temperature of the metal–liquid mixture at equilibrium is 28.3°C. What is the specific heat of the liquid? Neglect the heat capacity of the container.

Explanation:

Hello,

In this case, since silver is initially hot as it cools down, the heat it loses is gained by the liquid, which can be thermodynamically represented by:

That in terms of the heat capacities, masses and temperature changes turns out:

Since no phase change is happening. Thus, solving for the heat capacity of the liquid we obtain:

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the correct answer would be b) volume versus temperature, because they are also directly proportional.