2. If T(x, y) is the temperature at a point (x,y) on a thin metal plate in the xy-plane, then the level curves of T are ca isothermal curves. Along such a curve, the temperature remains constant. Given that 2 T(x,y) = V2x² + y² sketch the equipotential curves at which T = 2.0, T = 1.0, and T = 0.5.
Latent heat and phase change
A physical process in which a conversion among the basic states or phases of matter, i.e., solid, liquid, and gas takes place under the effect of a certain temperature and pressure is referred to as a phase change. Generally, the phase change of a substance occurs when heat transfer takes place between the substance and its surroundings. Based on the direction in which heat transfer takes place, different types of phase changes can occur.
Triple Point of Water
The branch of physics in which observer deals with temperature related properties is called thermodynamics.
Boiling Point of Water
Everyday examples of boiling is, boiling milk, heating water. One would have observed that when we heat water it goes through various stages and at one point bubbles show in water, and water keeps splashing with bubbles bursting, we in layman terms say that water is boiling.
Freezing Point of Water
In general, the freezing point of water is 0° Celsius, or 32° Fahrenheit. This is the temperature at which water will ordinarily change from its liquid state to its solid state (ice). However, there are certain conditions that can affect the freezing point of water. For example, a liquid may be supercooled or contain impurities so that it does not freeze at the ordinary freezing point.
![### Isothermal Curves on a Thin Metal Plate
**Problem Statement:**
2. If \( T(x, y) \) is the temperature at a point \((x, y)\) on a thin metal plate in the \(xy\)-plane, then the level curves of \( T \) are called **isothermal curves**. Along such a curve, the temperature remains constant. Given that
\[
T(x, y) = \frac{2}{\sqrt{2x^2 + y^2}}
\]
sketch the equipotential curves at which \( T = 2.0 \), \( T = 1.0 \), and \( T = 0.5 \).
**Graph Explanation:**
- The graph is a coordinate plane with \( x \)- and \( y \)-axes marked with arrows indicating the positive direction.
- A grid overlays the coordinate plane, aiding in sketching and plotting the curves.
- The goal is to sketch isothermal curves for the given temperatures.
**Analysis:**
To determine the shape of the curves, solve for \( \sqrt{2x^2 + y^2} \) using the given \( T \). For each \( T \), the eqaution becomes:
- For \( T = 2.0 \):
\[
\frac{2}{\sqrt{2x^2 + y^2}} = 2.0 \Rightarrow \sqrt{2x^2 + y^2} = 1
\]
- For \( T = 1.0 \):
\[
\frac{2}{\sqrt{2x^2 + y^2}} = 1.0 \Rightarrow \sqrt{2x^2 + y^2} = 2
\]
- For \( T = 0.5 \):
\[
\frac{2}{\sqrt{2x^2 + y^2}} = 0.5 \Rightarrow \sqrt{2x^2 + y^2} = 4
\]
These equations describe ellipses centered at the origin.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F603f265d-e012-4a8f-9345-c7d757ad85e7%2Fea5da98f-8aef-464b-96b1-ff2f54897f70%2Fnip416h_processed.png&w=3840&q=75)
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