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 12a

Chapter 19, Problem 12a

A rapidly spinning paddle wheel raises the temperature of 200 mL of water from 21°C to 25°C. How much heat is transferred?

Verified step by step guidance

Step 1: Understand the problem. The paddle wheel increases the temperature of water, and we need to calculate the heat transferred. The formula to use is the specific heat equation:

Q = mcΔT

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

Step 2: Convert the volume of water (200 mL) to mass. Since the density of water is approximately 1 g/mL, the mass of 200 mL of water is 200 g. Convert this to kilograms for SI units:

m = 200 \, \(\text{g}\) = 0.2 \, \(\text{kg}\)

Step 3: Identify the specific heat capacity of water. The specific heat capacity of water is approximately

c = 4186 \, \(\text{J/kg°C}\)

Step 4: Calculate the temperature change, ΔT. The initial temperature is 21°C, and the final temperature is 25°C. Therefore,

ΔT = 25 - 21 = 4 \, \(\text{°C}\)

Step 5: Substitute the values into the formula

Q = mcΔT

. Use

m = 0.2 \, \(\text{kg}\)

c = 4186 \, \(\text{J/kg°C}\)

, and

ΔT = 4 \, \(\text{°C}\)

. Perform the multiplication to find the heat transferred.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

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 the heat transfer in the given scenario, as it allows us to relate the temperature change to the amount of heat absorbed by the water.

Heat Transfer Equation

The heat transfer equation, often expressed as Q = mcΔT, relates the heat transferred (Q) to the mass (m) of the substance, its specific heat capacity (c), and the change in temperature (ΔT). In this case, ΔT is the difference between the final and initial temperatures of the water. This equation is fundamental for determining how much heat is transferred to the water as it is heated by the paddle wheel.

Mass of Water

The mass of water is essential for calculating heat transfer, as it directly influences the total heat absorbed. Since the density of water is approximately 1 g/mL, 200 mL of water has a mass of about 200 grams. Knowing the mass allows us to apply the heat transfer equation accurately, ensuring that we account for the total amount of water being heated in the process.

Recommended video:

Guided course

20:32

Mass Spectrometers

Related Practice

Textbook Question

500 J of heat energy are transferred to a gas during a process in which the gas expands at constant pressure from 400 cm³ to 800 cm³. The gas's thermal energy increases by 300 J during this process. What is the gas pressure?

views

Textbook Question

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

views

Textbook Question

How much heat energy must be added to a 6.0-cm-diameter copper sphere to raise its temperature from −50°C to 150°C?

Textbook Question

One way you keep from overheating is by perspiring. Evaporation—a phase change—requires heat, and the heat energy is removed from your body. Evaporation is much like boiling, only water's heat of vaporization at 35°C is a somewhat larger 24×10⁵ J/kg because at lower temperatures more energy is required to break the molecular bonds. Very strenuous activity can cause an adult human to produce 30 g of perspiration per minute. If all the perspiration evaporates, rather than dripping off, at what rate (in J/s) is it possible to exhaust heat by perspiring?

views

Textbook Question

Draw a first-law bar chart (see Figure 19.12) for the gas process in FIGURE EX19.7.

Textbook Question

80 J of work are done on the gas in the process shown in FIGURE EX19.3. What is V₁ in cm³?

views