(II) The heat capacity, C, of an object is defined as the...

(II) The heat capacity, $C,$ of an object is defined as the amount of heat needed to raise its temperature by 1 $\mathrm{C}^{\circ} .$ Thus, to raise the temperature by $\Delta T$ requires heat $Q$ given by $$Q=C \Delta T$$ (a) Write the heat capacity $C$ in terms of the specific heat, $c,$ of the material. $(b)$ What is the heat capacity of 1.0 $\mathrm{kg}$ of water? $(c)$ Of 35 $\mathrm{kg}$ of water?

(II) The heat capacity, $C,$ of an object is defined as the amount
of heat needed to raise its temperature by 1 $\mathrm{C}^{\circ} .$ Thus, to raise
the temperature by $\Delta T$ requires heat $Q$ given by
$$Q=C \Delta T$$
(a) Write the heat capacity $C$ in terms of the specific heat, $c,$
of the material. $(b)$ What is the heat capacity of 1.0 $\mathrm{kg}$ of
water? $(c)$ Of 35 $\mathrm{kg}$ of water?

Key Concepts

Relationship between Heat Capacity and Specific Heat

The relationship between heat capacity and specific heat is based on the mass of the substance. Specifically, the heat capacity of an object is obtained by multiplying the specific heat of the material by its mass (C = c·m). This equation shows that for a given material, the total amount of energy needed to change its temperature depends directly on both its specific heat value and its mass, encapsulating how material properties and quantity jointly influence thermal energy storage.

Heat Capacity

Heat capacity is the amount of heat required to change the temperature of an object by a given amount, typically by one degree Celsius. It is an extensive property of the object, meaning it depends on the amount of matter present. Heat capacity provides insight into how much energy a material can store as thermal energy when its temperature changes, and is generally represented by the formula Q = C?T, where Q is the heat added or removed, C is the heat capacity, and ?T is the temperature change.

Specific Heat

Specific heat is an intensive property of a material that indicates the amount of heat required to change the temperature of a unit mass of the substance by one degree Celsius. Unlike heat capacity, specific heat does not depend on the total mass or quantity of the material, making it a characteristic property that allows comparison across different substances. It is commonly expressed in units such as J/(kg·°C).

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