### Understanding Heat Transfer and Specific HeatWhen a body is heated, the rate at which its temperature changes depends on the material. The thermal energy needed to change the temperature of a body by \(\Delta T\) is determined by the equation:\[ \Delta Q = mc\Delta T \]where \(\Delta Q\) is the thermal energy, \(c\) is the specific heat of the material, and \(m\) is the mass of the body. The specific heat is the thermal energy needed to raise the temperature of 1 gram of material by one degree.### Heat Exchange ProcessIf a hot metal block is placed in cold water in a container, the metal block will cool, and the water and the container will warm. Eventually, the system will be at a final equilibrium temperature. The process can be expressed as:\[ \text{Heat gained} = \text{Heat lost} \]\[ [\text{Heat Gained by the container and water}] = [\text{Heat lost by the metal block}] \]### Formulating the EquationsThe initial temperature \(T_i\) of the water and the container, the initial temperature of the metal block \(T_B\), the final temperature of the system \(T_f\), the specific heat of the container, and the specific heat of the metal block are related by the following equation:\[ (c_{\text{con}} m_{\text{con}} + c_{\text{water}} m_{\text{water}}) (T_f - T_i) = c_{\text{block}} m_{\text{block}} (T_B - T_f) \] (Equation 1)### Problem-Solving Scenarios#### A. Different MaterialsIf the metal block and the container are made of different materials, and the specific heat of the container is known, derive the expression for calculating the specific heat of the block:\[ c_{\text{block}} = \]#### B. Same MaterialIf the container and the block are made of the same material, they will have the same specific heat, so \(c_{\text{block}} = c_{\text{con}}\). Equation (1) becomes:\[ (c_{\text{block}} m_{\text{con}} + c_{\text{water}} m_{\text{water}}) (T_f - T_i) = c_{\

Given:mass of block, mblockmass of container, mconmass of water, mwaterspecific heat of block,…

When a body is heated, how fast the temperature of the body changes depends on the material. The thermal energy needed to change the temperature of a body by AT' is determined by the equation AQ=mcT where AQ is the thermal energy, c is the specific heat of the material, and m is the mass of the body. The specific heat is the thermal energy needed to raise the temperature of 1 gram material by one degree. If a hot metal block is put into cold water in a container, the metal block will be cooled, and the water and the container will be warmed. Eventually, the system will be at a final temperature when thermal equilibrium is reached. The process can be expressed as

When a body is heated, how fast the temperature of the body changes depends on the material. The thermal energy needed to change the temperature of a body by AT' is determined by the equation AQ=mcT where AQ is the thermal energy, c is the specific heat of the material, and m is the mass of the body. The specific heat is the thermal energy needed to raise the temperature of 1 gram material by one degree. If a hot metal block is put into cold water in a container, the metal block will be cooled, and the water and the container will be warmed. Eventually, the system will be at a final temperature when thermal equilibrium is reached. The process can be expressed as

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter18: Temperature

Section: Chapter Questions

Problem 1P

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Similar questions

A person inhales and exhales 2.00 L of 37.0C air, evaporating 4.00102g of water from the lungs and breathing passages with each breath. (a) How much heat transfer occurs due to evaporation in each breath? (b) What is the rate of heat transfer in watts if the person is breathing at a moderate rate of 18.0 breaths per minute? (c) If the inhaled air had a temperature of 20.0C, what is the rate of heat transfer for warming the air? (d) Discuss the total rate of heat transfer as it relates to typical metabolic rates. Will this breathing be a major form of heat transfer for this person?
In 1986, a gargantuan iceberg broke away from the Ross Ice Shelf in Antarctica. It was approximately a rectangle 160 km long, 40.0 km wide, and 250 m thick. (a) What is the mass of this iceberg, given that the density of ice is 917kg/m3 ? (b) How much heat transfer (in joules) is needed to melt it? (c) How many years would it take sunlight alone to melt ice this thick, if the ice absorbs an average of 100W/m2, 12.00 h per day?
Unreasonable Results (a) Calculate the rate of heat transfer by conduction through a window with an area of 1.00 m2 that is 0.750 cm thick, if its inner surface is at 22.00C and its outer surface is at 35.00C (b) What is unreasonable about this result? (c) Which premise or assumption is responsible?
Assume you are measuring the specific heat of a sample of originally hot metal by using a calorimeter containing water. Because your calorimeter is not perfectly insulating, energy can transfer by heat between the contents of the calorimeter and the room. To obtain the most accurate result for the specific heat of the metal, you should use water with which initial temperature? (a) slightly lower than room temperature (b) the same as room temperature (c) slightly higher than room temperature (d) whatever you like because the initial temperature makes no difference
What does it mean to say that two systems are in thermal equilibrium?
Pressure cookers increase cooking speed by raising the boiling temperature of water above its value at atmospheric pressure. (a) What pressure is necessary to raise the boiling point to 120.0C ? (b) What gauge pressure does this correspond to?
A high-end gas stove usually has at least one burner rated at 14 000 Btu/h. (a) If you place a 0.25-kg aluminum pot containing 2.0 liters of water at 20.C on this burner, how long will it take to bring the water to a boil, assuming all the heat from the burner goes into the pot? (b) Once boiling begins how much time is required to boil all the water out of the pot?
Unreasonable Results (a) An automobile mechanic claims that an aluminum rod fits loosely into its hole on an aluminum engine block because the engine is hot and the rod is cold. If 1he hole is 10.0% bigger in diameter than the 22.0C rod, at what temperature will the rod be the same size as the hole? (b) What is unreasonable about this temperature? (2) Which premise is responsible?
(a) What is the rate of heat conduction through the 3.00-cm-thick fur of a large animal having a 1.40m2 surface area? Assume that the animal’s skin temperature is 32.0C, that tile air temperature is 5.00C, and that fur has the same thermal conductivity as air. (b) What food intake will the animal need in one day to replace this heat transfer?
Unreasonable Results Suppose the relative humidity is 80% on a day when the temperature is 30.0C. (a) What will the relative humidity be if the air cools to 25.0C and the vapor density remains constant? (b) What is unreasonable about this result? (c) Which premise is responsible?
Compare the SI units of specific heat and latent heat and explain any differences.
How is heat transfer related to temperature?