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Ch 17: Temperature and Heat
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경
17장, 문제 51

An asteroid with a diameter of 10 km and a mass of 2.60 × 1015 kg impacts the earth at a speed of 32.0 km/s, landing in the Pacific Ocean. If 1.00% of the asteroid's kinetic energy goes to boiling the ocean water (assume an initial water temperature of 10.0°C), what mass of water will be boiled away by the collision? (For comparison, the mass of water contained in Lake Superior is about 2 × 1015 kg.)

검증된 단계별 안내
1
Calculate the kinetic energy (KE) of the asteroid using the formula: \( KE = \frac{1}{2}mv^2 \), where \( m \) is the mass of the asteroid and \( v \) is its velocity. Convert the velocity from km/s to m/s before substituting into the formula.
Determine the amount of kinetic energy that goes into boiling the water. Since 1.00% of the asteroid's kinetic energy is used, multiply the total kinetic energy by 0.01.
Calculate the energy required to boil water. This involves two steps: first, calculate the energy needed to raise the temperature of the water from 10.0°C to 100.0°C using the specific heat capacity of water \( c = 4.18 \text{ J/g°C} \). Use the formula \( Q_1 = mc\Delta T \), where \( \Delta T = 100.0°C - 10.0°C \).
Next, calculate the energy required to convert water at 100.0°C to steam at 100.0°C using the latent heat of vaporization \( L = 2260 \text{ J/g} \). Use the formula \( Q_2 = mL \).
Set the total energy used for boiling (from step 2) equal to the sum of the energies calculated in steps 3 and 4 (\( Q_1 + Q_2 \)), and solve for the mass \( m \) of the water that is boiled away.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
8m

주요 개념

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

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion, calculated using the formula KE = 0.5 * m * v^2, where m is mass and v is velocity. In this scenario, the asteroid's kinetic energy is crucial for determining how much energy is transferred to the ocean water upon impact.
추천 영상:
가이드 코스
06:07
Intro to Rotational Kinetic Energy

Heat Transfer and Phase Change

Heat transfer involves the movement of thermal energy from one object to another, often resulting in a change of state, such as boiling. The energy required to boil water is determined by its specific heat and latent heat of vaporization, which are essential for calculating the mass of water boiled away by the asteroid's impact.
추천 영상:
가이드 코스
10:40
Latent Heat & Phase Changes

Energy Conversion Efficiency

Energy conversion efficiency refers to the percentage of energy that is successfully converted from one form to another. In this problem, only 1.00% of the asteroid's kinetic energy is used to boil the ocean water, highlighting the importance of understanding how energy is distributed and utilized in physical processes.
추천 영상:
가이드 코스
07:46
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