Ch. 19 - Heat and the First Law of Thermodynamics

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

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Giancoli Douglas 5th edition

Ch. 19 - Heat and the First Law of Thermodynamics

Problem 99d

Chapter 19, Problem 99d

Calculate what will happen when 1000 J of heat is added to 100 grams of water at 100°C.

Verified step by step guidance

Step 1: Identify the key concepts involved in the problem. Here, the problem involves heat transfer, phase change, and the specific heat of water. Since the water is already at 100°C, any additional heat will go into changing the phase of water from liquid to vapor (boiling), not increasing its temperature.

Step 2: Recall the formula for heat transfer during a phase change:

Q = mL

, where

Q

is the heat added,

m

is the mass of the substance, and

L

is the latent heat of vaporization. For water, the latent heat of vaporization is approximately

2260 \, \(\text{J/g}\)

Step 3: Convert the mass of water from grams to kilograms if necessary. In this case, the mass is already given in grams (

100 \, \(\text{g}\)

), so no conversion is needed.

Step 4: Use the formula

Q = mL

to determine how much of the water will vaporize. Rearrange the formula to solve for the mass of water vaporized:

m = \(\frac{Q}{L}\)

. Substitute

Q = 1000 \, \(\text{J}\)

and

L = 2260 \, \(\text{J/g}\)

into the equation.

Step 5: Calculate the result to determine how much of the 100 grams of water will vaporize. If the heat provided is insufficient to vaporize all the water, the remaining water will stay in liquid form. Ensure the units are consistent throughout the calculation.

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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 water, this value is approximately 4.18 J/g°C. Understanding this concept is crucial for calculating temperature changes when heat is added or removed from a substance.

Phase Changes

Phase changes occur when a substance transitions between solid, liquid, and gas states, often involving significant energy transfer without a temperature change. For water, adding heat at 100°C can lead to boiling, where the temperature remains constant while the water changes from liquid to vapor, requiring additional energy known as the latent heat of vaporization.

Thermodynamics

Thermodynamics is the branch of physics that deals with heat, work, and energy transfer. It encompasses laws that describe how energy is conserved and transformed. In this context, understanding the first law of thermodynamics helps explain how the added heat affects the water's temperature and phase, ensuring energy conservation throughout the process.

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