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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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