VII. Questions 1. Write an expression for the length (L) of the rod at any tempe
ID: 1318402 • Letter: V
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VII. Questions 1. Write an expression for the length (L) of the rod at any temperature (T) as a function of L , T, T and a where T, is some initial temperature and T is the final temperature to which the rod has been heated. 2. Why did we use metal tubes instead of metal rods? 3. Why it is acceptable to measure the full length of the sample rod with a meter stick. but the change in length due to the thermal expansion must be measured using a micrometer? 4. A cold block of metal feels colder than a block of wood at the same temperature. Why?Explanation / Answer
4)When you put your finger on an object that is colder than the surface of your finger, heat energy will be transferred from the surface of your finger into the surface of the object, until the temperatures are equalized, by the process of conduction. At the same time, heat energy will be transferred from the interior of your finger to the cooling surface of your finger, and heat energy will be transferred from the warming surface of the object into the interior of the object. The rate of energy transfer will depend on the difference in temperature - large temperature differences will accelerate the energy transfer, but as the temperatures become closer, the rate will slow down.
The amount of energy you need to put into a fixed mass of a material to warm it up by a certain temperature increment is known as the material's specific heat capacity. Let's look at two common metals. Aluminum has a specific heat capacity of 0.90 J/(g?K) - that is, you need to put 0.90 J into 1 g of aluminum to raise its temperature by 1 K (remember that an increment of 1 Kelvin is the same as an increment of 1 degree Celsius). Steel has a specific heat capacity of 0.49 J/(g?K). Wood, on the other hand, has a specific heat capacity of about 1.7 J/(g?K) (with a range of between 1.2 and 2.3 J/(g?K), depending on the species of wood and how dry it is).
Let's assume for a moment that your finger is entirely at one temperature, and the object is entirely at a lower temperature - and as the temperatures of your finger and the object equilibrate, the temperature in each remains uniform. So, assuming you have equal masses of wood and metal, you need to put more energy into the wood to raise its temperature - maybe 2 to 4 times as much energy. That means the temperature of the wood will raise more slowly, so the equilibrium temperature of your finger and the wood will be lower.
But your finger and the object do not have uniform temperatures. The thermal energy transferred from the surface of your finger to the surface of the object will be conducted through the object, at a rate determined by the conductivity of the object. The thermal conductivity of aluminum is about 225 W/(m?K) - remember that a watt (unit of power) is equal to a Joule (unit of energy) per second, so we're saying that if you have a bar of aluminum 1 meter long, with one end at a temperature 1 Kelvin higher than the other end, the rate of energy transfer from one end of the bar to the other will be 225 Joules per second. Steel has a thermal conductivity of about 45 W/(m?K). The thermal conductivity of wood is about 0.2 W/(m?K). So, thermal energy moves much more slowly in wood than it does in metal - about 200 times more slowly than steel, and 1000 times more slowly than aluminum!
What that means is, when you put your finger on wood, you're going to warm up a very small mass of wood near the contact area, and the thermal energy won't move away from that spot very quickly. So, that small mass of wood will come nearly into thermal equilibrium with your finger very rapidly, at a temperature near the temperature your finger started at. If you wait a very long time, the thermal energy will move out into the rest of the wood, slowing bringing down the equilibrium temperature, but your body is generating heat energy to warm your finger back up to it's normal point that whole time.
But when you put your finger on metal, because the thermal energy is being conducted through the metal quickly, you're warming up a much larger mass of metal. Even though metal has a lower specific heat, when you multiply that by a much larger mass, you require more energy! So the temperature of the metal rises more slowly, and the equilibrium temperature of your finger and the metal will be closer to the original temperature of the metal.
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