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At what temperature does the numerical reading on a Celsius thermometer equal that on a Fahrenheit thermometer?

$$-40^{\circ} \mathrm{C}$$

Chemistry 101

Chapter 1

Chemistry: The Study of Change

Intro to Chemistry

Carleton College

Drexel University

University of Maryland - University College

Lectures

02:29

Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry deals with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds. Chemistry also involves understanding the properties and interactions of individual atoms and molecules for use in larger-scale applications.

04:42

In chemistry and physics, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic particles, and in everyday as well as scientific usage, "matter" generally includes atoms and anything made up of them, and any particles and objects that act as if they have both rest mass and volume. However it does not include massless particles such as photons, or other energy phenomena or waves such as light or sound. Matter exists in various states (known as phases) that are defined by various physical properties, such as state of matter, phase, shape, and density. The Standard Model of particle physics and the general theory of relativity describe fundamental particles and the fundamental forces acting between them that control the structure and dynamics of matter.

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Hi. So this question is kind of interesting question is actually more of a math question than any chemistry question, but it does deal with temperature. So that's, I guess, chemistry related. So basically, they want you to find the temperature at which the numerical reading on a Celsius thermometer will equal the numerical reading on a fair and high thermometer. So first wishes right out our equation to get the relationship between Fahrenheit and Celsius. So degrees Fahrenheit equals 9/5 times degrees Celsius plus 32. Right now, how can we solve for this number that we don't know this number in which Fahrenheit equal Celsius, all by making fair hind cells your equal in this equation and then solving for it? Right? So we have to make Fahrenheit equal to Celsius, and it's just a sign that some random variable right? Since it's all the same number, let's assign it t just some random temperature that we don't know yet. So plugging t for both Fahrenheit and for Celsius. So 9/5 t plus 32 okay, and then we could just solve for this. Just do some simple algebra. We subtract. Um, let's see Let's subtract 9/5 t from both sides. Then we'll get negative or over five. T equals 32. Okay. And you can multiply both sides by negative 5/4, Right? Too simple, uh, change and or simple. Just simplifying algebraic simplification. And then you'll get negative. T equals negative 40 degrees Fahrenheit or degrees Celsius. Right, Because this is the temperature. I wish you the same. So this is our answer. Let's just circle. One of them would just circle degrees Celsius. And this is the temperature at which they will read the same at negative 40 degrees Celsius, 4 F. So this was a pretty interesting question. Made you think a little bit about just solving math equations. And just think about temperature stuff and hope this is helpful, you know? Yeah. Thanks for listening.

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