A lab student drops a 400.0-g piece of metal at $120.0 ^ { \circ } \mathrm { C }$ into a cup containing 450.0 g of water at $15.0 ^ { \circ } \mathrm { C }$ After waiting for a few minutes, the student measures that the final temperature of the system is $40.0 ^ { \circ } \mathrm { C }$ What is the specific heat of the metal, assuming that no significant heat is exchanged with the surroundings or the cup? The specific heat of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } .$

Question

A lab student drops a  400.0-g piece of metal at $120.0 ^ { \circ } \mathrm { C }$ into a cup containing  450.0 g of water at $15.0 ^ { \circ } \mathrm { C }$ After waiting for a few minutes, the student measures that the final temperature of the system is $40.0 ^ { \circ } \mathrm { C }$ What is the specific heat of the metal, assuming that no significant heat is exchanged with the surroundings or the cup? The specific heat of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } .$

Quizplus · Accepted Answer

The heat lost by the metal is equal to the heat gained by the water. Using the formula $q = mc\Delta T$, where $q$ is the heat transferred, $m$ is the mass, $c$ is the specific heat capacity, and $\Delta T$ is the change in temperature, we can set the heat lost by the metal equal to the heat gained by the water and solve for the specific heat of the metal. Given that the final temperature is $40.0^\circ C$, the change in temperature for the water is $40.0^\circ C - 15.0^\circ C = 25.0^\circ C$ and for the metal is $120.0^\circ C - 40.0^\circ C = 80.0^\circ C$. The mass of the water is $0.450 \,kg$ and the mass of the metal is $0.400 \,kg$. The specific heat of water is given as $4186 \,J/kg\cdot K$. Setting the heat gained by the water equal to the heat lost by the metal and solving for the specific heat of the metal, $c_m$, gives:$$0.450 \,kg \times 4186 \,J/kg\cdot K \times 25.0 \,K = 0.400 \,kg \times c_m \times 80.0 \,K$$Solving for $c_m$ yields approximately $1470 \,J/kg\cdot K$.

A Lab Student Drops a 400 120.0∘C120.0 ^ { \circ } \mathrm { C }120.0∘C

A Lab Student Drops a 400 $120.0 ^ { \circ } \mathrm { C }$