91影视

Mass of water,$m=250\text{g}$

Specific heat of water,$c=1{\text{鈥塩补濒.驳}}^{\text{-1}}{\text{K}}^{\text{-1}}$

Initial temperature,$T_1={24}^0\text{C}$

Final temperature,$T_2={20}^0\text{C}$

The first energy transfer takes place between the chunk of metal and the boiling water at temperature ${100}^0\text{C}$. The next energy transfer takes place between the metal and the water in the Styrofoam cup that was at temperature ${20}^0\text{C}$.

The heat absorbed $Q$by the water from the hot metal is given by the expression,

$\begin{array}{l}Q=mc\left(T_2鈭�T_1\right)\\ Q=250脳1脳\left(4\right)\\ \boxed{Q=1000\text{鈥塩补濒}}\end{array}$

The only energy transfer is heat transfer, thus the heat absorbed by the water is 1000 cal.

Heat capacity 鈥� It is defined as the ratio of heat absorbed to the change in the temperature.

Specific heat 鈥� It is the heat that is needed to raise the temperature of a unit mass to$1^0\text{C}$.

Energy transfer between two bodies is due to the difference in temperature of the bodies.

The heat transfer takes place until the two bodies acquire an equilibrium state and the amount of heat absorbed by water is equal to the heat lost by the metal.

The heat lost by the metal is the heat absorbed by the water, that is -1000 cal.

Initial temperature,$T_1={100}^{\text{0}}\text{C}$

Final temperature,$T_2={24}^{\text{0}}\text{C}$

Amount of energy gained by the chunk,$\text{Q}=鈭�1000\text{cal}$

The heat capacity of the metal is given by the expression,

$\begin{array}{l}C=\frac{Q}{T_2鈭�T_1}\\ C=\frac{鈭�1000}{\begin{array}{l}24鈭�100\\ =\frac{鈭�1000}{鈭�76}\\ =13.157\text{cal}鈰�{\text{K}}^{\text{-1}}\end{array}}\end{array}$

The heat capacity of the metal chunk is calculated as $\boxed{C=13.157{\text{cal.g}}^{\text{-1}}{\text{K}}^{\text{-1}}}$.

Heat capacity of the metal,$C=13.157\text{cal}鈰�{\text{K}}^{\text{-1}}$

Mass of the metal,$m=100\text{鈥塯}$

$\begin{array}{l}c=\frac{C}{m}\\ c=\frac{13.157}{100}\\ c=0.131{\text{cal.g}}^{\text{-1}}{\text{K}}^{\text{-1}}\end{array}$

Specific heat capacity of the 100 g mass of metal is calculated as $\boxed{c=0.131{\text{cal.g}}^{\text{-1}}{\text{K}}^{\text{-1}}}$.