 Classical Mechanics

Specific heat

Consider an aluminium cup with mass $140.0 \text{ g}$ at $60 ^\circ\text{C}$ and water with a mass of $600.0 \text{ g}$ contained in this cup at the same temperature. If the temperature of both the cup and water decreases to $57 ^\circ\text{C},$ approximately how much energy is removed from the cup-water system?

The specific heat of water and aluminuim are $4187 \text{ J/kg}\cdot\text{K}$ and $900 \text{ J/kg}\cdot\text{K},$ respectively.

If we immerse a steel ball with mass $0.8 \text{ kg}$ initially at $800 \text{ K}$ into a styrofoam box containing $35.0 \text{ kg}$ of water at $300 \text{ K},$ what is the approximate final temperature of the water at equilibrium, assuming that water was not vaporized and the water-steel ball system is thermally isolated?

The specific heat of water and steel are $4187 \text{ J/kg}\cdot\text{K}$ and $448 \text{ J/kg}\cdot\text{K},$ respectively.

Consider a steel H-beam with mass $130.0 \text{ kg}$ and length $10.0 \text{ m}.$ If it absorbs a thermal energy of $1.8 \times 10^6 \text{J},$ what is the approximate increase in the length of the H-beam, assuming that the specific heat of steel is $c=448 \text{ J/kg}\cdot\text{K}$ and the the coefficient of linear expansion for steel is $\alpha=11.0 \times 10^{-6} \text{ K}^{-1}?$

If a certain metal with mass $0.40 \text{ kg}$ absorbs $3.0 \text{ kJ}$ of energy by heat, the temperature of the metal rises by $17.0 ^\circ\text{C}.$ What is the approximate specific heat of the metal?

Approximately how much heat must be absorbed by water of mass $m=450.0 \text{ g}$ at $0^\circ\text{C}$ to increase its temperature to $27 ^\circ\text{C}?$

The specific heat of water is $4187 \text{ J/kg}\cdot\text{K}.$

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