# Specific Heat (slope and steepness)

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1 1 Specific Heat (slope and steepness) 10 pages. According to the Physical Science text book, the Specific Heat of a material is DEFINED as the following: Specific heat is the amount of heat energy required to raise the temperature of ONE gram of a material by 1 0 C, and a characteristic property of a material. Is this statement VE~~~~~~RY clear to you? I can explain MUCH, MUCH, MUCH clearer than this! Yes, I can! Read the following! So, let us bring in here 1 gram of water and also 1 gram of sand, each in a beaker. Let us assume that both materials (water and sand) have the temperature exactly 20 degrees Celsius. This is the initial temperature. Put each beaker on a heater as shown below. 1 gram 1 gram of sand of water Heater Heater From the pictures right above, it appears that the amount of sand is much more than that of the water? Does this seem strange to you? But the drawings are actually CORRECT! Why? Because both are exactly ONE gram! The very initial temperature of both materials (sand and water) is 20 degrees Celsius. We now increase the temperature of both materials by exactly ONE degree in Celsius by adding heat to both materials with the heaters so that the temperature of both materials now

2 2 becomes 21 degrees. Do we have to add the same amount of heat to both materials (both are exactly 1 gram) to raise their temperature by ONE degree Celsius? No! Although both are ONE gram, we MUST add much more heat to the water than to the sand to raise their temperature ONE degree Celsius. To raise the temperature of 1 gram of water by ONE degree, we MUST add 1.00 Calorie of heat to the water. To raise the temperature of 1 gram of sand by ONE degree, we MUST add 0.19 Calories of heat to the sand, which is much less than 1.00 Calories! We say that the value of the specific heat of water is 1.00 Calories/g 0 C. We say that the value of the specific heat of sand is 0.19 Calories/g 0 C This EXPERIMENTAL FACT indicates that 1 gram of water requires much MORE heat to raise its temperature by ONE degree than 1 gram of sand. Conversely, 1 gram of sand requires much LESS heat to raise its temperature by ONE degree than 1 gram of water. This is what it means when we say that the specific heat of water is much greater than the specific heat of sand. Please go to the next page. Thank you.

3 The value of slope does NOT represent the specific heat! What does this mean? 3 Temperature Sand Value of specific heat is 0.19 Cal./g 0 C Water Value of specific heat is 1.00 Cal./g 0 C Time The slope represents how quickly temperature rises. The temperature of sand increases more quickly than the water does. That is, the slope of the graph for sand is greater than the slope of the graph for water. But, the value of the specific heat is OPPOSITE to this tendency. The value of the specific heat of sand (0.19) is LESS than that of water (1.00)! The greater the slope (steeper), the less is the specific heat. The less the slope (less steep), the greater is the specific heat. Sand (smaller value of specific heat) warms up very quickly (greater slope). That why, it is not comfortable to walk with barefoot on the sand of beach in hot summer day. On the other hand, the ocean (Water, larger value of specific heat) warms up very slowly (less slope). One more thing I want to tell you. On the next page.

4 Prepare sand and water 10 grams each and heat them. 4 Temperature Sand (10 grams) 15 0 C 10 0 C 5 0 C 5 0 C Water (10 grams) 5 0 C Minutes 5 minutes 20 minutes To increase temperature from 10 degrees to 15 degrees in Celsius (increase by 5 degrees), sand takes 5 minutes, while water takes 20 minutes. Water takes 4 times longer than sand to increase temperature by 5 degrees. Takes more time means more heat are added. Therefore, water absorbed more heat than sand did to raise temperature by 5 degrees (from 10 0 C to 15 0 C) Move onto the next page.

5 5 Temperature Boiling point C C Melting point C Amount of heat added This graph does NOT represent water, Some substance other than water. But why? Because????????? Look at the graph for WATER on the next page. Then you can tell. Time Region Region Region Solid Phase (Below freezing point, single phase) Temperature increases as heat is added Mixture of solid phase and liquid phase (Melting region) Temperature NEVER changes even though heat is continuously added. Why? Answer! Liquid Phase (single phase) Temperature increases as heat is added Region Region 4 5 Mixture of liquid phase and gas phase (Boiling region) Temperature NEVER changes even though heat is continuously added. Why? Answer! Gas Phase (single phase) Temperature increases as heat is added Continues the next page

6 6 Temperature C C Melting period (Mixture of ICE and liquid water) Amount of heat added Boiling period (Mixture of liquid water and gaseous water or water vapor) This is strictly for WATER. Compare this graph with the graph on the preceding page. Can you see the differences? Time In the graph above (for WATER), the horizontal axis is the time axis (the time increases from left to right). Temperature sensor ICE Heater To computer Please go to the next page. Thank you.

8 8 collide). This is the GAS state of water or water vapor. Thus, during MELTING PERIOD (region 2), the bonds (the attractive forces) between the particles are just weakened but not completely disrupted. On the other hand, during BOILING PERIOD (region 4), the bonds (the attractive forces) between the particles are COMPLETELY disrupted and every one of the particles become completely free from the other particles. This is the GAS phase of water, which is called the water vapor. Graph on page 6 shows that the the boiling period is much longer than the melting period. This means that to vaporize liquid water completely requires much more heat energy than to melt the ice of the same mass completely. Questions; 1. Which region requires the largest amount of heat to raise the temperature by the same amount? 2. Which region has the largest value of Specific-Heat? 3. Which region requires the least amount of heat to raise the temperature by the same amount? 4. Which region has the least value of Specific Heat? You cannot answer these questions unless you REALLY understand the Specific Heat. The specific heat of a substance is; The amount of heat required to raise the temperature if 1 gram substance by ONE degree. Move onto the next page.

9 Question: You place a pot of water on the stove and set the knob to high (about C). Eventually, the temperature of the water remains constant at C and the water boils (this occurs in the region 4 on the graph of page 6.) DRAW micro I/O energy diagram for the boiling water (during a phase change) Answer: During boiling process, since the temperature does NOT change, the AVERAGE kinetic energy of the particles does NOT change either. But since the bonds between the particles are being broken and the particles are made FREE (the particles become far, far, and far apart!), the potential energy increases. HC interaction Heat Energy Water- Particles at 373 K Increase in potential energy. (constant temperature) There is NO change in AVERAGE kinetic energy. WHY? EXPLAIN! The LAW of conservation energy says: Energy Input = Energy Output + Change in energy In our present case, this law becomes: Heat Energy = Increase in Potential Energy That is, ALL added heat is 100% used to increase the potential energy. NONE of the added heat is used to raise the temperature. One more question on the next page

10 NEXT question: 10 A student pours herself a glass of cold water and takes a few sips. Using a thermometer, she measures the temperature of the water and finds it is 3 C. The student leaves the glass of cold water sitting on the kitchen counter (at room temperature, 25 C) while she goes on a brief errand. When she returns, she notices the remaining water tastes warmer than before. Using a thermometer, she measures the temperature of the water and finds it is 20 C. During this period (the temperature increases from 3 C to 20 C), DRAW micro I/O energy diagram for the water. This is NOT during phase change. Heat Conduction interaction Heat Energy Water particles at 20 C Increase in AVERAGE kinetic energy and Increase in Potential energy In this case, BOTH average kinetic energy and potential energy increase! Why? Because the temperature (The AVERAGE kinetic energy) increases. Because the temperature increases, the particles move faster and they become more separated. Consequently the potential energy increases also. The particles become MORE far apart. Energy is required to make them far apart. This energy is provided from the added heat (Heat energy input). FAR APART means that attractive POTENTIAL ENERGY increases.

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