Topics for Today Thermal expansion (18-3) Absorption of Heat (18-4) Someone left an article of clothing at the last exam, please see me if it is yours.

Thermal Expansion Most materials expand as the temperature increases. A temperature change of ΔT produces a change in length of ΔL = Lα ΔT, where α is the “coefficient of linear expansion”. The change in length is proportional to the origin length – why? Typically α ≈ 10-5/°C for metals. The change in length will occur for all dimensions of an object. Since Volume = Length3, the change in volume is ΔV = V β ΔT, where β = “coefficient of volume expansion” = 3α. Do demo 4A30.20 - Expansion & Contraction Demo - Ball and Ring.

Thermal Expansion An engineering application of thermal expansion is the bimetal strip thermostat. If you bond together two different materials with different thermal expansion coefficients, then they will bend as the temperature changes. Many thermostats use a bimetal strip, or more usually a bimetal coil, as the temperature sensing elements. A mercury switch turns on/off according to the ambient temperature.

Thermal Expansion A square plate made of lead has an oval-shaped hole. The oval may be described by the lengths a and b as shown in the drawing. Which of the following correctly describes the plate after its temperature is increased by two hundred Celsius degrees? The size of the plate will increase, but a and b will both decrease. The size of the plate will remain unchanged, but a and b will both increase. The size of the plate will increase, and a and b will both increase. The size of the plate will remain unchanged, but a and b will both decrease. The size of the plate will increase, but only a will increase.

Absorption of Heat Heat is energy that is transferred between a system and the environment or another system. Heat is transferred from the higher temperature system to the lower temperature one. Heat is measured in units of Joules, calories, kilocalories, and British thermal units (BTUs). 1 cal = 4.1868 J. “Calories” on food labels are actually kilocalories and are a measure of the energy that your body can produce by eating the food.

Heat Capacity If a system absorbs heat (Q) and the temperature of the system increases by Δ𝑇= 𝑇 𝑓 − 𝑇 𝑖 , then 𝑄=𝐶Δ𝑇 where C is the heat capacity of the system. For a system made out of a given material, we can calculate the heat capacity by multiplying the mass, m, of the system times the “specific heat”, c, of the material, 𝐶=𝑐𝑚. The heat capacity of water is c = 1 cal/g∙°C, it takes on 1 cal of heat to increase the temperature of 1 gram of water by 1 °C. Water has an unusually high heat capacity.

Specific Heat We fill one beaker with 800 grams of water and the other with 400 grams of water and 400 grams of lead. We heat both beakers equally. In which beaker will the temperature rise faster? A) beaker with all water B) beaker with half water/half lead C) the temperatures will rise at the same rate Do demo 4B10.10 - Heat Capacity Demo

Heat Capacity A swimming pool has a width of 9.0 m and a length of 12.0 m. The depth of the water is 1.83 m. One morning, the temperature of the pool water was 15.0 C. The water then absorbed 2.00  109 J of heat from the Sun. What is the final temperature of the water? Assume no heat loss to the surroundings. 16.9 C 18.1 C 17.4 C 19.6 C 20.2 C Specific heat of water is 4187 J/kg∙K

Heat of Transformation Sometimes heat goes into changes the state of a system rather than changing its temperature, for example, heating an ice cube will change the ice to water, but the water will stay at 0 C until all of the ice is melted. Solid, liquid, and gas are different “phases”. Melt = solid → liquid Freeze = liquid → solid Evaporate/vaporize = liquid → gas Condense = gas → liquid Sublimate = solid → gas Deposit = gas → solid

Heat of Transformation “Heat of transformation” or “latent heat” (L) is the heat per unit mass needed for the phase change. To melt a mass (m) of ice at 0 C into water at 0 C, the heat needed is Q = Lm, with L = 333.9 kJ/kg. Heats of transformation are named for the phase change, e.g “heat of fusion” or “heat of vaporization”.

Heat of Transformation

Heat Capacity Four 1-kg cylinders are heated to 100 C and placed on top of a block of paraffin wax, which melts at 63 C. There is one cylinder made from lead, one of copper, one of aluminum, and one of silver. After a few minutes, it is observed that the cylinders have sunk into the paraffin to differing depths. Which cylinder will sink deepest? Lead Copper Aluminum Silver