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Chapter 2: Problem 16

If a system has 60 J of heat added to it, resulting in a change of internal energy of 40 J, what is the work done by the system? A. 50 J B. 20 J C. 30 J D. 60 J

Short Answer

Expert verified
The work done by the system is 20 J, so the correct answer is B.

Step by step solution

01

Understanding the First Law of Thermodynamics

The first law of thermodynamics is given by the formula: \[ \triangle U = Q - W \] where \( \triangle U \) is the change in internal energy, \( Q \) is the heat added to the system, and \( W \) is the work done by the system.
02

Identify Known Values

From the problem, we know that the heat added to the system (\( Q \)) is 60 J and the change in internal energy (\( \triangle U \)) is 40 J.
03

Rearrange the Formula

To find the work done by the system (\( W \)), rearrange the formula \( \triangle U = Q - W \) to solve for \( W \): \[ W = Q - \triangle U \]
04

Substitute the Given Values

Substitute the known values into the rearranged equation: \[ W = 60 \text{ J} - 40 \text{ J} \]
05

Calculate the Work Done

Perform the subtraction to find \( W \): \[ W = 20 \text{ J} \]
06

Select the Correct Answer

Compare the calculated work done (20 J) to the given options. The correct answer is B. 20 J.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Internal Energy
Internal energy refers to the total energy contained within a system. It's all the energy from microscopic sources like the movement of molecules and the energy in chemical bonds. When a system undergoes any process, its internal energy may change. This change is often symbolized as \(\triangle U\). If energy is added to the system, this might increase \(\triangle U\), while if energy is taken away, \(\triangle U\) decreases. For example, in the given exercise, the internal energy change is mentioned as 40 J. This means that the total energy inside the system has increased by 40 J due to the process.
Heat Transfer
Heat transfer is the process where thermal energy is exchanged between systems. It's typically measured in Joules (J), like in the exercise where 60 J of heat is added to the system. Heat can flow in or out of a system in various ways, such as conduction, convection, or radiation. In our exercise, heat transfer is symbolized as \( Q \). The First Law of Thermodynamics includes this heat term to account for energy changes due to thermal interactions. So, if you add 60 J of heat to a system, it will affect the system's energy balance.
Work Done
Work done by a system refers to the energy transferred when the system exerts a force over a distance. It's symbolized as \( W \) and also measured in Joules (J). According to the First Law of Thermodynamics, the work done by a system can be calculated if you know the heat added to the system and the change in internal energy, using the formula: \[ W = Q - \triangle U \]. In our exercise, we calculated the work done by substituting the values, \( Q = 60 \text{ J} \) and \( \triangle U = 40 \text{ J} \). The result was \( W = 20 \text{ J} \), showing that 20 J of energy has been used by the system to do work on the surroundings.

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