7 min read•december 30, 2022
Krish Gupta
Daniella Garcia-Loos
Krish Gupta
Daniella Garcia-Loos
refers to how well an object can transfer thermal energy. Objects that have high are good conductors of heat and vice versa. of a substance is given by the letter k.
Here are some key points about :
Metals tend to have a much higher value of than organic solids, liquids and gases. This is partly due to the sea of electrons and metallic bonding in metals as opposed to the covalent bonding found in many non-metals.
Let’s look at an example. Let’s say you are out on a sunny day and you decide to go fishing. You have a metal fishing pole and a wooden fishing pole. Let’s say you have been fishing for a while now. You’d expect both the fishing poles to be the same temperature as the environment because heat would have flown until was established.
You would be right. If you measured the temperatures of either fishing poles using a thermometer you’d get the same number. BUT if you were to touch each fishing pole which one do you think would feel hotter? The metal one right? So why is it that the metal feels hotter than wood even though they are at the same temperature? This is because a metal has a much higher than wood so it transfers heat to your hand much faster.
The same would be true on a winter day. If you left a plastic water bottle and a metal water bottle out in the month of December you’d feel that the metal one is much colder even though truly they are at the same temperature. This is because metal is great at transferring heat so it sucks the heat out of your hand much faster than wood.
Here are some key points about the of metals:
Now that we know that objects with greater allow for faster heat flow, we need an equation to find how much faster? 10 times? 100 times?
To answer that question we have Fourier’s Conduction Law: Q/Δt=kAΔT/L
This law states that the rate at which heat flows depends on the of teh object, the cross sectional area and the . The is defined as the ratio of the temperature difference to the length of the object 🧮 Since this is not a calculus course, we can assume that the rate of heat flow is the same across the object or even across a junction of two objects.
Here are some key points about :
Example Problem:
You are asked to design an experiment to measure the of two different metals, aluminum and copper. The aluminum sample has a thickness of 0.5 cm, and the copper sample has a thickness of 0.75 cm.
(a) Describe the experimental setup you would use to measure the of the aluminum and copper samples.
To solve this problem, you could follow these steps:
(a) Design an experimental setup to measure the of the aluminum and copper samples. One way to do this would be to use a hot plate to heat one end of each sample, and a thermocouple to measure the temperature at the hot and cold ends of the sample. You could place the samples on a thermally insulating surface to minimize heat loss to the surroundings.
(b) Measure the across the samples by placing the thermocouple at the hot and cold ends of the sample and recording the temperature readings. To obtain accurate results, you would need to control for factors such as the temperature of the hot plate, the distance between the hot and cold ends of the sample, and the time elapsed during the measurement.
(c) Calculate the of each metal from the data you collect using the formula Q = -kA(dT/dx)/L, where Q is the heat flow through the sample, k is the of the material, A is the cross-sectional area of the sample, dT/dx is the across the sample, and L is the thickness of the sample. To calculate the heat flow (Q), you could measure the power of the hot plate and the time elapsed during the measurement, and use the formula Q = P*t. To calculate the cross-sectional area (A) of the sample, you could measure the width and height of the sample.
(d) Based on your calculations, you would expect copper to have a higher than aluminum. This is because copper has a higher atomic weight and a more ordered crystal structure than aluminum, which allows it to conduct heat more efficiently.
(e) Some sources of error that could affect the accuracy of your measurements include:
Cross-sectional area (A)
: Cross-sectional area refers to the measure of an object's surface area when cut perpendicular to its length or height. In physics, it plays an important role in determining how much heat can be transferred through conduction.Fourier's Conduction Law
: Fourier's conduction law describes how heat flows through a solid material by conduction. It states that the rate at which heat transfers through a material is directly proportional to the temperature gradient (change in temperature per unit distance) and inversely proportional to its thermal conductivity.Heat flow (Q)
: Heat flow, represented by Q, is the transfer of thermal energy from one object to another due to a difference in temperature. It is measured in units of joules (J).Power (P)
: Power refers to the rate at which work is done or energy is transferred. It measures how quickly a task can be completed or how fast energy is being used.Temperature gradient
: Temperature gradient refers to the change in temperature per unit distance. It measures how quickly or slowly temperature changes across a given space.Thermal Conductivity
: Thermal conductivity refers to how well a material conducts or transfers heat. It measures how quickly thermal energy can move through a substance.Thermal Equilibrium
: Thermal equilibrium refers to a state where two or more objects are at the same temperature and there is no net flow of heat between them. In this state, thermal energy is evenly distributed among all objects involved.Thickness (L)
: Thickness refers to the distance between two surfaces of an object or material. It is a measure of how thick or thin something is.Time elapsed (t)
: Time elapsed refers to the duration or amount of time that has passed since an event started or occurred.Valence electrons
: Valence electrons are the outermost electrons in an atom that participate in chemical bonding. They determine the reactivity and chemical properties of an element.7 min read•december 30, 2022
Krish Gupta
Daniella Garcia-Loos
Krish Gupta
Daniella Garcia-Loos
refers to how well an object can transfer thermal energy. Objects that have high are good conductors of heat and vice versa. of a substance is given by the letter k.
Here are some key points about :
Metals tend to have a much higher value of than organic solids, liquids and gases. This is partly due to the sea of electrons and metallic bonding in metals as opposed to the covalent bonding found in many non-metals.
Let’s look at an example. Let’s say you are out on a sunny day and you decide to go fishing. You have a metal fishing pole and a wooden fishing pole. Let’s say you have been fishing for a while now. You’d expect both the fishing poles to be the same temperature as the environment because heat would have flown until was established.
You would be right. If you measured the temperatures of either fishing poles using a thermometer you’d get the same number. BUT if you were to touch each fishing pole which one do you think would feel hotter? The metal one right? So why is it that the metal feels hotter than wood even though they are at the same temperature? This is because a metal has a much higher than wood so it transfers heat to your hand much faster.
The same would be true on a winter day. If you left a plastic water bottle and a metal water bottle out in the month of December you’d feel that the metal one is much colder even though truly they are at the same temperature. This is because metal is great at transferring heat so it sucks the heat out of your hand much faster than wood.
Here are some key points about the of metals:
Now that we know that objects with greater allow for faster heat flow, we need an equation to find how much faster? 10 times? 100 times?
To answer that question we have Fourier’s Conduction Law: Q/Δt=kAΔT/L
This law states that the rate at which heat flows depends on the of teh object, the cross sectional area and the . The is defined as the ratio of the temperature difference to the length of the object 🧮 Since this is not a calculus course, we can assume that the rate of heat flow is the same across the object or even across a junction of two objects.
Here are some key points about :
Example Problem:
You are asked to design an experiment to measure the of two different metals, aluminum and copper. The aluminum sample has a thickness of 0.5 cm, and the copper sample has a thickness of 0.75 cm.
(a) Describe the experimental setup you would use to measure the of the aluminum and copper samples.
To solve this problem, you could follow these steps:
(a) Design an experimental setup to measure the of the aluminum and copper samples. One way to do this would be to use a hot plate to heat one end of each sample, and a thermocouple to measure the temperature at the hot and cold ends of the sample. You could place the samples on a thermally insulating surface to minimize heat loss to the surroundings.
(b) Measure the across the samples by placing the thermocouple at the hot and cold ends of the sample and recording the temperature readings. To obtain accurate results, you would need to control for factors such as the temperature of the hot plate, the distance between the hot and cold ends of the sample, and the time elapsed during the measurement.
(c) Calculate the of each metal from the data you collect using the formula Q = -kA(dT/dx)/L, where Q is the heat flow through the sample, k is the of the material, A is the cross-sectional area of the sample, dT/dx is the across the sample, and L is the thickness of the sample. To calculate the heat flow (Q), you could measure the power of the hot plate and the time elapsed during the measurement, and use the formula Q = P*t. To calculate the cross-sectional area (A) of the sample, you could measure the width and height of the sample.
(d) Based on your calculations, you would expect copper to have a higher than aluminum. This is because copper has a higher atomic weight and a more ordered crystal structure than aluminum, which allows it to conduct heat more efficiently.
(e) Some sources of error that could affect the accuracy of your measurements include:
Cross-sectional area (A)
: Cross-sectional area refers to the measure of an object's surface area when cut perpendicular to its length or height. In physics, it plays an important role in determining how much heat can be transferred through conduction.Fourier's Conduction Law
: Fourier's conduction law describes how heat flows through a solid material by conduction. It states that the rate at which heat transfers through a material is directly proportional to the temperature gradient (change in temperature per unit distance) and inversely proportional to its thermal conductivity.Heat flow (Q)
: Heat flow, represented by Q, is the transfer of thermal energy from one object to another due to a difference in temperature. It is measured in units of joules (J).Power (P)
: Power refers to the rate at which work is done or energy is transferred. It measures how quickly a task can be completed or how fast energy is being used.Temperature gradient
: Temperature gradient refers to the change in temperature per unit distance. It measures how quickly or slowly temperature changes across a given space.Thermal Conductivity
: Thermal conductivity refers to how well a material conducts or transfers heat. It measures how quickly thermal energy can move through a substance.Thermal Equilibrium
: Thermal equilibrium refers to a state where two or more objects are at the same temperature and there is no net flow of heat between them. In this state, thermal energy is evenly distributed among all objects involved.Thickness (L)
: Thickness refers to the distance between two surfaces of an object or material. It is a measure of how thick or thin something is.Time elapsed (t)
: Time elapsed refers to the duration or amount of time that has passed since an event started or occurred.Valence electrons
: Valence electrons are the outermost electrons in an atom that participate in chemical bonding. They determine the reactivity and chemical properties of an element.© 2024 Fiveable Inc. All rights reserved.
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