### Temperature as a Measure of Kinetic Energy [block_16] 1. Have you ever wondered what makes a cup of hot coffee feel warm in your hands? The answer lies in the invisible dance of molecules. 2. These particles are moving, colliding, and transferring energy, creating the heat you feel. 3. But how can we quantify this energy? > This is where **temperature **comes in. **Temperature **is a direct measure of the average kinetic energy of the particles in a substance. ### The Kelvin Scale: Directly Proportional to Kinetic Energy [block_18] 1. In science, the **Kelvin scale **is the **standard **unit of temperature because it directly correlates with the average kinetic energy of particles. 2. On this scale, **absolute zero (0 K) **represents the point where particles have no kinetic energy: they are completely motionless (in theory). 3. This makes the Kelvin scale an "**absolute**" temperature scale, ideal for scientific calculations. The relationship between temperature in Kelvin and the average kinetic energy ($E_k$) of particles is: $$ E_k \propto T(K) $$ > This proportionality means that if the Kelvin temperature of a substance doubles, the average kinetic energy of its particles also doubles. [{"_key":"block_24","_type":"block","asset":null,"children":[{"_key":"CAHOrKTdx1dUnzpKdfOfMc","_type":"span","markDefs":[],"marks":[],"text":"Absolute zero (0 K or -273.15°C) is a "},{"_key":"39c0bd040634","_type":"span","markDefs":[],"marks":["strong"],"text":"theoretical temperature"},{"_key":"130aefdc3408","_type":"span","markDefs":[],"marks":[],"text":" at which all particle motion stops. "}],"level":1,"listItem":"bullet","markDefs":[],"style":"normal"},{"_key":"10e80c5354c6","_type":"block","asset":null,"children":[{"_key":"fdce5d89faa5","_type":"span","markDefs":[],"marks":[],"text":"While unattainable in practice, it serves as a crucial reference point for understanding temperature."}],"level":1,"listItem":"bullet","markDefs":[],"style":"normal"}] ![](https://cdn.sanity.io/images/w7j7fz60/production/c9906d7196591d830df2f474e6860f9340d34eca-1048x862.png) ### Relationship Between Kelvin and Celsius [block_26] 1. The Kelvin and Celsius scales are closely **related**, differing only in their **starting points**. 2. While the Celsius scale is based on the freezing (0°C) and boiling points (100°C) of water, the Kelvin scale starts at **absolute zero**. The conversion formula is: $$ T(K) = T(°C) + 273.15 $$ [{"_key":"58bd28c8c3e3","_type":"block","asset":null,"children":[{"_key":"6b221ce0bec9","_type":"span","markDefs":[],"marks":[],"text":"Water freezes at 0°C, which is equivalent to $0 + 273.15 = 273.15 \\, \\text{K}$."}],"level":2,"listItem":"bullet","markDefs":[],"style":"normal"},{"_key":"6be9c3c59a46","_type":"block","asset":null,"children":[{"_key":"c9e28a93658b","_type":"span","markDefs":[],"marks":[],"text":"Water boils at 100°C, which is $100 + 273.15 = 373.15 \\, \\text{K}$."}],"level":2,"listItem":"bullet","markDefs":[],"style":"normal"}] [{"_key":"block_34","_type":"block","asset":null,"children":[{"_key":"87d1d1861b08","_type":"span","markDefs":[],"marks":[],"text":"Convert 25°C to Kelvin:\n$$\nT(K) = 25 + 273.15 = 298.15 \\, \\text{K}\n$$"}],"markDefs":[],"style":"normal"}] [{"_key":"block_36","_type":"block","asset":null,"children":[{"_key":"CAHOrKTdx1dUnzpKdfOfNq","_type":"span","markDefs":[],"marks":[],"text":"Do not confuse the size of a Kelvin unit with a Celsius degree. Both scales have the same incremental size (1 K = 1°C), but their starting points differ."}],"markDefs":[],"style":"normal"}] ![](https://cdn.sanity.io/images/w7j7fz60/production/7883f723dcaa3cea670dcbf21225041098428690-974x862.png) ### Observable Changes During Temperature Changes [block_37] 1. When the temperature of a substance changes, the kinetic energy of its particles changes as well. 2. This can lead to several observable effects: #### **Expansion or Contraction of Matter** [block_39] 1. As particles **gain **kinetic energy, they **move **more vigorously and occupy more space, causing expansion. 2. Conversely, when particles **lose **energy, they **slow down** and take up less space, leading to contraction. [{"_key":"c70a1eeaf02b","_type":"block","asset":null,"children":[{"_key":"767b5e8a0547","_type":"span","markDefs":[],"marks":[],"text":"A balloon inflates when heated because the gas particles inside move faster and push outward."}],"level":2,"listItem":"bullet","markDefs":[],"style":"normal"},{"_key":"7dd4a0ae18a2","_type":"block","asset":null,"children":[{"_key":"6360e6dbdd37","_type":"span","markDefs":[],"marks":[],"text":"A metal rod contracts when cooled due to the reduced motion of its particles."}],"level":2,"listItem":"bullet","markDefs":[],"style":"normal"}] [{"_key":"block_45","_type":"block","asset":null,"children":[{"_key":"CAHOrKTdx1dUnzpKdfOfP4","_type":"span","markDefs":[],"marks":[],"text":"Think of a crowded dance floor: when the music speeds up ("},{"_key":"721cf7146287","_type":"span","markDefs":[],"marks":["strong"],"text":"higher temperature"},{"_key":"3fc063ad99cb","_type":"span","markDefs":[],"marks":[],"text":"), people move more energetically and need more space ("},{"_key":"5433d8009199","_type":"span","markDefs":[],"marks":["strong"],"text":"expansion"},{"_key":"95fffc4a2ec2","_type":"span","markDefs":[],"marks":[],"text":"). "}],"level":1,"listItem":"bullet","markDefs":[],"style":"normal"},{"_key":"61230b97f89d","_type":"block","asset":null,"children":[{"_key":"bab4f1ecbd2e","_type":"span","markDefs":[],"marks":[],"text":"When the music slows down ("},{"_key":"3d701839b719","_type":"span","markDefs":[],"marks":["strong"],"text":"lower temperature"},{"_key":"2121af2f5c8d","_type":"span","markDefs":[],"marks":[],"text":"), they calm down and take up less space ("},{"_key":"f85b11f9c703","_type":"span","markDefs":[],"marks":["strong"],"text":"contraction"},{"_key":"35808ab4ea03","_type":"span","markDefs":[],"marks":[],"text":")."}],"level":1,"listItem":"bullet","markDefs":[],"style":"normal"}] ![](https://cdn.sanity.io/images/w7j7fz60/production/f8dcb99a03195f898f52bec2189680af6eafe323-1524x856.png) #### **Changes in Physical State** [block_47] 1. Temperature changes can also cause substances to **transition **between **states of matter **(solid, liquid, gas). 2. These transitions are directly tied to the **energy **of the particles: 1. **Melting**: Solid to liquid (particles gain energy and overcome rigid bonds). 2. **Boiling**: Liquid to gas (particles gain enough energy to escape intermolecular forces). 3. **Freezing**: Liquid to solid (particles lose energy and settle into a fixed structure). [{"_key":"block_54","_type":"block","asset":null,"children":[{"_key":"CAHOrKTdx1dUnzpKdfOfQI","_type":"span","markDefs":[],"marks":[],"text":"When ice melts into water, the particles absorb energy to break free from their fixed positions in the solid lattice. "}],"level":1,"listItem":"bullet","markDefs":[],"style":"normal"},{"_key":"d358d86e29f2","_type":"block","asset":null,"children":[{"_key":"78078fcf124a","_type":"span","markDefs":[],"marks":[],"text":"This energy absorption occurs without a temperature change until all the ice has melted."}],"level":1,"listItem":"bullet","markDefs":[],"style":"normal"}] [{"_key":"block_56","_type":"block","asset":null,"children":[{"_key":"CAHOrKTdx1dUnzpKdfOfRW","_type":"span","markDefs":[],"marks":[],"text":"Changes of state like melting and boiling occur at constant temperatures because the energy added is used to "},{"_key":"3ca1a221c7dd","_type":"span","markDefs":[],"marks":["strong"],"text":"overcome intermolecular forces"},{"_key":"19277d98c076","_type":"span","markDefs":[],"marks":[],"text":" rather than increasing kinetic energy."}],"markDefs":[],"style":"normal"}] [{"_key":"block_58","_type":"block","asset":null,"children":[{"_key":"CAHOrKTdx1dUnzpKdfOfSk","_type":"span","markDefs":[],"marks":[],"text":"What happens to the kinetic energy of particles when a substance transitions from a liquid to a gas?"}],"markDefs":[],"style":"normal"}] ### Energy Changes During a Phase Change [cba03f3911aa] 1. During a phase change, energy is transferred but does not result in a temperature change. 2. Instead, the energy is used to **break or form intermolecular bonds**, altering the state of the substance. #### Key Energy Changes: [eb63a60b8fcb] 1. **Melting (Solid to Liquid)**: Energy is absorbed to break the bonds holding particles in a fixed structure. 2. **Freezing (Liquid to Solid)**: Energy is released as particles lose kinetic energy, forming stronger intermolecular bonds. 3. **Boiling (Liquid to Gas)**: Energy is absorbed to overcome attractive forces, allowing particles to move freely as a gas. 4. **Condensation (Gas to Liquid)**: Energy is released as particles slow down and intermolecular forces pull them closer together. [{"_key":"6e05ce0fa72e","_type":"block","asset":null,"children":[{"_key":"06dcd1c6b85c","_type":"span","marks":[],"text":"During a phase change, the energy added or removed is called "},{"_key":"2f3c8c8028b4","_type":"span","marks":["strong"],"text":"latent heat"},{"_key":"54338a829ddd","_type":"span","marks":[],"text":" and affects the potential energy of the particles, not their kinetic energy, which explains the constant temperature."}],"markDefs":[],"style":"normal"}] ### Heating Curve Example: [60af7774aa27] 1. **Flat regions**: Phase changes where temperature remains constant while energy is used to break or form bonds. 2. **Sloped regions**: Temperature changes as kinetic energy increases or decreases. ![](https://cdn.sanity.io/images/w7j7fz60/production/a3fa3479222d7d06cc074fb107a991a42484a600-1670x1132.png) [{"_key":"008eb4b6d63e","_type":"block","asset":null,"children":[{"_key":"994032bc3d9b","_type":"span","marks":[],"text":"Many students assume temperature always increases when energy is added."}],"level":1,"listItem":"bullet","markDefs":[],"style":"normal"},{"_key":"ac84e38ed2af","_type":"block","asset":null,"children":[{"_key":"7718ab27127c","_type":"span","marks":[],"text":"However, during a phase change, "},{"_key":"27c0f24dd0fd","_type":"span","marks":["strong"],"text":"energy alters the structure"},{"_key":"76ef2799a616","_type":"span","marks":[],"text":", not the kinetic energy of particles."}],"level":1,"listItem":"bullet","markDefs":[],"style":"normal"}] [{"_key":"c3f2b268d4de","_type":"block","asset":null,"children":[{"_key":"43a5277429ba0","_type":"span","marks":[],"text":"Heat vs. Temperature:"}],"markDefs":[],"style":"h4"},{"_key":"17302f5333e6","_type":"block","asset":null,"children":[{"_key":"7f87e5685d9b0","_type":"span","marks":["strong"],"text":"Heat"},{"_key":"7f87e5685d9b1","_type":"span","marks":[],"text":" is the total energy transferred due to a temperature difference, related to both the kinetic energy and the number of particles in a substance. It depends on mass and is measured in joules (J)."}],"level":1,"listItem":"bullet","markDefs":[],"style":"normal"},{"_key":"ae079b863a56","_type":"block","asset":null,"children":[{"_key":"3867833c42b80","_type":"span","marks":["strong"],"text":"Temperature"},{"_key":"3867833c42b81","_type":"span","marks":[],"text":" measures the average kinetic energy of particles in a substance, independent of mass, and is measured in degrees Celsius (°C) or Kelvin (K)."}],"level":1,"listItem":"bullet","markDefs":[],"style":"normal"}] [{"_key":"ea4890e31522","_type":"block","asset":null,"children":[{"_key":"bcf5a0ee1abf","_type":"span","markDefs":[],"marks":[],"text":"Convert $-50 \\, \\text{°C}$ to Kelvin: $$T(K) = -50 + 273.15 = 223.15 \\, \\text{K}$$"}],"level":1,"listItem":"bullet","markDefs":[],"style":"normal"},{"_key":"3b6584dac57d","_type":"block","asset":null,"children":[{"_key":"7f6773cbb55d","_type":"span","markDefs":[],"marks":[],"text":"Convert $310 \\, \\text{K}$ to Celsius: $$T(\\text{°C}) = 310 - 273.15 = 36.85 \\, \\text{°C}$$"}],"level":1,"listItem":"bullet","markDefs":[],"style":"normal"},{"_key":"block_67","_type":"block","asset":null,"children":[{"_key":"76da6da105a3","_type":"span","markDefs":[],"marks":[],"text":"What is the Kelvin equivalent of $100 \\, \\text{°C}$?"}],"level":1,"listItem":"bullet","markDefs":[],"style":"normal"}] ### [block_76]