Ch. 19 - Heat and the First Law of Thermodynamics

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 19 - Heat and the First Law of Thermodynamics

Problem 100b

Chapter 19, Problem 100b

A 12-g lead bullet traveling at 220 m/s passes through a thin wall and emerges at a speed of 160 m/s. If the bullet absorbs 50% of the heat generated, If the bullet’s initial temperature was 20°C, will any of the bullet melt, and if so, how much?

Verified step by step guidance

Determine the kinetic energy lost by the bullet as it passes through the wall. Use the formula for kinetic energy:

E_{k} = \frac{1}{2} m v^{2}

, where

m

is the mass of the bullet and

v

is its velocity. Subtract the final kinetic energy from the initial kinetic energy to find the energy lost.

Calculate the heat energy absorbed by the bullet. Since the bullet absorbs 50% of the heat generated, multiply the energy lost by 0.5 to find the heat energy absorbed.

Determine the temperature increase of the bullet using the formula:

Q = m c ΔT

, where

Q

is the heat energy absorbed,

m

is the mass of the bullet,

c

is the specific heat capacity of lead (128 J/kg°C), and

ΔT

is the temperature change. Solve for

ΔT

Check if the final temperature of the bullet exceeds the melting point of lead (327°C). Add the temperature increase to the initial temperature (20°C) to find the final temperature.

If the final temperature exceeds the melting point, calculate the amount of lead that melts using the formula:

Q = m L_{f}

, where

L_{f}

is the latent heat of fusion for lead (24,500 J/kg). Subtract the heat required to raise the bullet to the melting point from the total heat absorbed, and use the remaining heat to calculate the mass of lead that melts.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion, calculated using the formula KE = 1/2 mv², where m is mass and v is velocity. In this scenario, the lead bullet's initial and final kinetic energies are crucial for determining the energy lost as it passes through the wall, which can then be related to the heat absorbed by the bullet.

Heat Transfer

Heat transfer refers to the movement of thermal energy from one object or substance to another, which can occur through conduction, convection, or radiation. In this case, the bullet absorbs 50% of the heat generated from its kinetic energy loss, and understanding this concept is essential to calculate how much energy is converted to heat and whether it is sufficient to raise the bullet's temperature to its melting point.

Melting Point

The melting point is the temperature at which a solid becomes a liquid. For lead, this temperature is approximately 327.5°C. By calculating the temperature increase of the bullet after absorbing heat, we can determine if it reaches or exceeds this melting point, indicating whether any of the bullet will melt.