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 16

Chapter 19, Problem 16

What is the maximum mass of ethyl alcohol you could boil with 1000 J of heat, starting from 20°C?

Verified step by step guidance

Step 1: Identify the relevant physical properties of ethyl alcohol. You need its specific heat capacity (c), boiling point, and heat of vaporization (L). For ethyl alcohol, c ≈ 2.44 J/(g·°C), boiling point ≈ 78°C, and L ≈ 846 J/g.

Step 2: Calculate the heat required to raise the temperature of ethyl alcohol from 20°C to its boiling point (78°C). Use the formula:

Q = m × c × ΔT

, where Q is the heat, m is the mass, c is the specific heat capacity, and ΔT is the temperature change.

Step 3: Determine the heat required to vaporize the ethyl alcohol once it reaches its boiling point. Use the formula:

Q = m × L

, where Q is the heat, m is the mass, and L is the heat of vaporization.

Step 4: Combine the two heat calculations from Steps 2 and 3. The total heat provided (1000 J) must equal the sum of the heat required to raise the temperature and the heat required to vaporize the ethyl alcohol. Set up the equation:

1000 = m × c × ΔT + m × L

Step 5: Solve for the mass (m) of ethyl alcohol. Rearrange the equation from Step 4 to isolate m, and substitute the known values for c, ΔT, and L. This will give you the maximum mass of ethyl alcohol that can be boiled with 1000 J of heat.

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Key Concepts

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

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 ethyl alcohol, this value is essential to determine how much energy is needed to increase its temperature from an initial state to its boiling point before phase change occurs.

Latent Heat of Vaporization

Latent heat of vaporization is the amount of heat required to convert a unit mass of a substance from liquid to gas at its boiling point without changing its temperature. This concept is crucial for calculating how much energy is needed to boil ethyl alcohol after it has reached its boiling point.

Energy Conservation

The principle of energy conservation states that energy cannot be created or destroyed, only transformed from one form to another. In this context, the total energy provided (1000 J) must be accounted for in both raising the temperature of ethyl alcohol and converting it to vapor, guiding the calculations for maximum mass that can be boiled.

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