Ch 17: Temperature and Heat

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경

Young & Freedman Calc 14th Edition

Ch 17: Temperature and Heat

문제 37

17장, 문제 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?

검증된 단계별 안내

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 = m c ΔT

, 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 = m c ΔT

, 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 = m L

, 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:

m c ΔT_{\(\text{iron}\)} = m c ΔT_{\(\text{water}\)} + m L

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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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.

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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