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Ch 17: Temperature and Heat
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo
Capitolo 17, Problema 37

A blacksmith cools a 1.20 kg chunk of iron, initially at 650.0°C, by trickling 15.0°C water over it. All of the water boils away, and the iron ends up at 120.0°C. How much water did the blacksmith trickle over the iron?

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Identify the heat lost by the iron as it cools from 650.0°C to 120.0°C. Use the formula for heat transfer: Q = mcΔT, where m is the mass of the iron, c is the specific heat capacity of iron, and ΔT is the change in temperature.
Calculate the heat required to boil the water. First, determine the heat needed to raise the temperature of the water from 15.0°C to 100.0°C using the formula: Q = mcΔT, where m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.
Next, calculate the heat required to convert the water at 100.0°C to steam at 100.0°C using the formula: Q = mL, where L is the latent heat of vaporization of water.
Set the heat lost by the iron equal to the total heat gained by the water (both to raise its temperature and to vaporize it). This gives the equation: mcΔT_{\(\text{iron}\)} = mcΔT_{\(\text{water}\)} + mL.
Solve the equation for the mass of the water m to find out how much water was trickled over the iron.

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Specific Heat Capacity

Specific heat capacity is the amount of heat required to change the temperature of a unit mass of a substance by one degree Celsius. It is crucial for calculating the heat lost by the iron as it cools from 650.0°C to 120.0°C. The specific heat capacity of iron allows us to determine the total heat energy transferred to the water.
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06:50
Specific Heat & Temperature Changes

Latent Heat of Vaporization

Latent heat of vaporization is the heat required to convert a unit mass of a liquid into vapor without a temperature change. In this scenario, it is essential for calculating the energy needed to boil away the water. Understanding this concept helps determine how much heat the water absorbs as it transitions from liquid to steam.
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10:40
Latent Heat & Phase Changes

Conservation of Energy

Conservation of energy states that energy cannot be created or destroyed, only transferred or converted from one form to another. This principle is vital in solving the problem, as the heat lost by the iron must equal the heat gained by the water. By applying this concept, we can set up an equation to find the mass of water needed to absorb the heat lost by the iron.
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06:24
Conservation Of Mechanical Energy
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