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Chapter 15: Problem 4

A model steam engine of \(1.00-\mathrm{kg}\) mass pulls eight cars of \(1.00-\mathrm{kg}\) mass each. The cars start at rest and reach a velocity of \(3.00 \mathrm{m} / \mathrm{s}\) in a time of \(3.00 \mathrm{s}\) while moving a distance of \(4.50 \mathrm{m} .\) During that time, the engine takes in $135 \mathrm{J}$ of heat. What is the change in the internal energy of the engine?

Short Answer

Expert verified
Answer: The change in internal energy of the engine is 99 J.

Step by step solution

01

Calculate the net force acting on the cars from the given information

First, let's find the net force acting on the cars. We know their initial velocity (u), final velocity (v), time taken (t), and mass (m), so we can use the equation of motion v = u + at to find the acceleration (a). Then we can use Newton's second law (F = ma) to find the force. v = 3.00 m/s u = 0 m/s t = 3.00 s Rearrange the equation of motion to solve for acceleration: a = (v - u) / t Plug the values into the equation: a = (3.00 - 0) / 3.00 a = 1.00 m/s虏 Now, find the net force on the cars using F = ma: F = (1.00 kg per car 脳 8 cars) 脳 1.00 m/s虏 F = 8.00 kg 脳 1.00 m/s虏 F = 8.00 N
02

Calculate the work done by the steam engine on the cars

Now that we have the net force acting on the cars, let's find the work done by the steam engine. We know the distance traveled by the cars (d) and the net force (F), so we can use the formula for work: W = F 脳 d. Plug the values into the equation: W = 8.00 N 脳 4.50 m W = 36.00 J
03

Apply the First Law of Thermodynamics to find the change in internal energy

Now that we have the work done by the system (W) and the heat absorbed (Q), we can use the First Law of Thermodynamics to find the change in internal energy (螖U). 螖U = Q - W Plug the values into the equation: 螖U = 135 J - 36.00 J 螖U = 99 J The change in the internal energy of the engine is 99 J.

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Most popular questions from this chapter

An ideal gas is in contact with a heat reservoir so that it remains at a constant temperature of \(300.0 \mathrm{K}\). The gas is compressed from a volume of \(24.0 \mathrm{L}\) to a volume of 14.0 L. During the process, the mechanical device pushing the piston to compress the gas is found to expend \(5.00 \mathrm{kJ}\) of energy. How much heat flows between the heat reservoir and the gas and in what direction does the heat flow occur?
The efficiency of an engine is \(0.21 .\) For every \(1.00 \mathrm{kJ}\) of heat absorbed by the engine, how much (a) net work is done by it and (b) heat is released by it?
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