/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 19 The specific heat of soil is \(0... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

The specific heat of soil is \(0.20 \mathrm{kcal} / \mathrm{kgC}^{\circ}\), and the specific heat of water is \(1.00 \mathrm{kcal} / \mathrm{kgC}^{\circ}\). This means that if \(1 \mathrm{~kg}\) of soil and \(1 \mathrm{~kg}\) of water each receives \(1 \mathrm{kcal}\) of energy, ideally, a. the water will be warmer than the soil by \(0.8^{\circ} \mathrm{C}\). b. the soil will be \(4^{\circ} \mathrm{C}\) warmer than the water. c. the soil will be \(5^{\circ} \mathrm{C}\) warmer than the water. d. the water will warm by \(1^{\circ} \mathrm{C}\), and the soil will warm by \(0.2^{\circ} \mathrm{C}\).

Short Answer

Expert verified
b. The soil will be \(4^{\circ} \mathrm{C}\) warmer than the water.

Step by step solution

01

Understanding Specific Heat

Specific heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius. For soil, it is given as \(0.20 \ \mathrm{kcal/kgC}^{\circ}\), and for water, it is \(1.00 \ \mathrm{kcal/kgC}^{\circ}\). This means it takes more energy to heat water by one degree compared to soil.
02

Applying the Formula

The change in temperature \(\Delta T\) can be calculated using the formula: \[ \Delta T = \frac{Q}{m \cdot c} \] where \(Q\) is the heat added (1 kcal in this case), \(m\) is the mass (1 kg), and \(c\) is the specific heat.
03

Calculating Temperature Change for Water

For water, using \(c = 1.00 \ \mathrm{kcal/kgC}^{\circ}\), the change in temperature \(\Delta T\) is \[ \Delta T = \frac{1 \ \mathrm{kcal}}{1 \ \mathrm{kg\cdot 1.00 \ \mathrm{kcal/kgC}^{\circ}}} = 1^{\circ} \mathrm{C}. \] So, the water will warm by \(1^{\circ} \mathrm{C}\).
04

Calculating Temperature Change for Soil

For soil, using \(c = 0.20 \ \mathrm{kcal/kgC}^{\circ}\), the change in temperature \(\Delta T\) is \[ \Delta T = \frac{1 \ \mathrm{kcal}}{1 \ \mathrm{kg\cdot 0.20 \ \mathrm{kcal/kgC}^{\circ}}} = 5^{\circ} \mathrm{C}. \] So, the soil will warm by \(5^{\circ} \mathrm{C}\).
05

Comparing Temperature Changes

Comparing the results: the soil warms by \(5^{\circ} \mathrm{C}\) while the water warms by \(1^{\circ} \mathrm{C}\). Therefore, the soil will be warmer than the water by \(4^{\circ} \mathrm{C}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

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

Heat Transfer
Heat transfer refers to the movement of thermal energy from one object or substance to another. This process can occur in three ways: conduction, convection, and radiation. When you feel the sun warming your skin, that's an example of heat transfer by radiation. When you hold a hot cup of coffee, the heat moving from the cup to your hand is heat transfer through conduction. In our exercise, when energy (heat) is added to both soil and water, the heat transfer causes a change in their temperatures.
  • Conduction: Direct heat transfer through a substance without movement.
  • Convection: Heat transfer through fluids by the movement of molecules.
  • Radiation: Heat transfer through electromagnetic waves.
Despite receiving the same amount of energy, soil and water react differently due to their specific heat capacities. This variance shows how different materials transfer heat differently.
Temperature Change
Temperature change is the result of heat transfer. When an object absorbs or loses heat, its temperature changes. The specific heat capacity plays a crucial role in determining how much the temperature will change. It tells us how much energy is needed to change the temperature of 1 kg of a substance by 1°C.
For instance:
  • A lower specific heat capacity means the temperature will change more with the same amount of energy.
  • A higher specific heat capacity means the temperature will change less.
In the case of our exercise, the specific heats of water and soil dictate their temperature changes when exposed to the same energy. Water, with a higher specific heat of 1.00 kcal/kg°C, will experience a smaller temperature rise compared to soil, which has a specific heat of 0.20 kcal/kg°C. This is why water heats up less than soil given the same energy input.
Energy Conservation
The principle of energy conservation is a fundamental concept in physics. According to this principle, energy cannot be created or destroyed, only transformed from one form to another. When heat is added to a substance, it is transformed into kinetic energy that increases the movement of particles, resulting in a temperature rise.
In our context:
  • 1 kcal of heat energy is being added to both soil and water, and it is used completely in raising their temperatures.
  • No energy is lost; it is just changing form, confirming energy conservation.
This exercise helps illustrate energy conservation by showing that the same amount of energy affects different substances in diverse ways due to their unique properties.
Thermal Properties
Thermal properties refer to the characteristics of a material that describe how it responds to heat. Understanding these properties helps to predict how materials behave when they absorb or lose heat energy. Key thermal properties include specific heat, thermal conductivity, and thermal expansion.
  • Specific Heat: Determines how much heat is needed to change the temperature of a material, as demonstrated in the exercise.
  • Thermal Conductivity: Measures how well a material can conduct heat.
  • Thermal Expansion: Describes how a material's dimensions change with temperature.
In this exercise, the focus is on specific heat, which shows that different materials will require different amounts of energy to achieve the same temperature change. This is why the temperature change in soil and water is different even when they receive the same heat input. Knowing these properties helps in applications like designing thermal systems and choosing materials based on their heat response.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The specific heat of water is \(1.00 \mathrm{cal} / \mathrm{gC}^{\circ}\), and the specific heat of ice is \(0.500 \mathrm{cal} / \mathrm{gC}^{\circ}\). The same amount of energy applied to equal masses, say, \(50.0 \mathrm{~g}\) of water and ice, will result in (assume the ice does not melt) a. a greater temperature increase for the water. b. a greater temperature increase for the ice. c. the same temperature increase for each. d. unknown results.

The work that a heat engine is able to accomplish is ideally equivalent to the a. difference between the heat supplied and the heat rejected. b. heat that was produced in the cycle. c. heat that appears in the exhaust gases. d. sum total of the heat input and the heat output.

The specific heat of copper is roughly three times as great as the specific heat of gold. Which of the following is true for equal masses of copper and gold? a. If the same amount of heat is applied, the copper will become hotter. b. Copper heats up three times as fast as gold. c. A piece of copper stores three times as much heat at the same temperature. d. The melting temperature of copper is roughly three times that of gold.

The evaporation of water cools the surroundings, and the condensation of this vapor a. does nothing. b. warms the surroundings. c. increases the value of the latent heat of vaporization. d. decreases the value of the latent heat of vaporization.

The transfer of heat that takes place by the movement of groups of molecules with higher kinetic energy is a. conduction. c. radiation. b. convection. d. sublimation.

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.