Ch 19: Work, Heat, and the First Law of Thermodynamics

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 19: Work, Heat, and the First Law of Thermodynamics

Problem 19a

Chapter 19, Problem 19a

Two cars collide head-on while each is traveling at 80 km/h. Suppose all their kinetic energy is transformed into the thermal energy of the wrecks. What is the temperature increase of each car? You can assume that each car's specific heat is that of iron.

Verified step by step guidance

Step 1: Convert the speed of each car from km/h to m/s. Use the conversion factor: 1 km/h = 1000 m/3600 s.

Step 2: Calculate the kinetic energy of each car using the formula:

E_{k} = (1/2) m v^{2}

, where

m

is the mass of the car and

v

is its velocity in m/s.

Step 3: Assume all the kinetic energy is converted into thermal energy. Use the formula for heat transfer:

Q = m c Δ T

, where

Q

is the thermal energy,

m

is the mass of the car,

c

is the specific heat capacity of iron, and

Δ T

is the temperature increase.

Step 4: Rearrange the heat transfer formula to solve for the temperature increase:

Δ T = Q / (m c)

. Substitute the value of

Q

(kinetic energy of the car),

m

(mass of the car), and

c

(specific heat capacity of iron, approximately 450 J/(kg·°C)).

Step 5: Perform the calculation using the values provided or assumed for the mass of the car and the specific heat capacity of iron to determine the temperature increase of each car.

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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 an object possesses due to its motion, calculated using the formula KE = 1/2 mv², where m is mass and v is velocity. In the context of the collision, each car has kinetic energy based on its speed of 80 km/h. This energy is crucial for understanding how much thermal energy is generated during the collision.

Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In this scenario, the kinetic energy of the moving cars is converted entirely into thermal energy upon collision, which is essential for calculating the resulting temperature increase of the wrecks.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. For this problem, the specific heat of iron is used to determine how much the temperature of each car increases after the collision, given the total thermal energy produced from the kinetic energy conversion.

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