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14 Cards in this Set
- Front
- Back
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crystalline solid model
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large number (10²³) of atoms held in a regular array by springs
the springs are electrical bonds between the atoms |
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relationship between temperature and distance between atoms of a solid material
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as temperature increases, distance between atoms increases
a few exceptions exist |
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linear expansion
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expansion in a single dimension
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formulaic expression of the relationship between temperature and distance between atoms of a solid material
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∆L = α L ∆T
L: length α: coefficient of linear expansion T: temperature |
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coefficient of linear expansion
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α
characteristic of each solid that describes how changes in temperature affect changes in length between atoms of a solid |
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coefficient of linear expansion formulas
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given ∆L = α L ∆T
α = 1∆L / L∆T = ∆L / L∆T α is therefore the fractional change in length per 1 degree of temperature change |
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thermistor
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device whose electrical resistance is very sensitive to its temperature
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thermistor & temperature
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thermistor measures in ohms (electrical resistance) which can be converted to temperature via a conversion table or graph
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converting ohms to °C
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Get the ohms
Get the resistance & temperature values from the table for the next highest & next lowest points Find the equation of the line between those 2 points T = T₁ + (T₂ - T₁) / (R₂ - R₁) * (R - R₁) round to nearest 2/10 of a degree |
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calculating percent accuracy
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has to do with the accuracy of the measuring devices
% accuracy α = (% Acc ∆L + % Acc L + % Acc ∆T) * 100 % Acc α = [ (0.01 mm / ∆L mm) + (1 mm / L mm) + (0.2 C / ∆T C) ] * 100 |
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Does the value of α depend on the units in which length is measured?
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No!
α = ∆L / L * ∆T The units for length are in the numerator & denominator one time and thus cancel |
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Does the value of α change when the temperature is measured in F instead of C?
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Yes!
Given the same arbitrary values for ∆L and L Farenheit @ boiling: 2/(4*212) = 0.00235849056 Celsius @ boiling: 2/(4*100) = 0.005 Because F is greater than C for any temperature above -40, the denominator will be larger, yielding a smaller α Also, ∆T_F = 9/5∆T_C shows that for any change in temperature, changes in F > changes in C |
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A steel bridge is 200 feet long when the temp is -15 °C. Find its length when the temp is 35 °C given a α = 1.2x10⁻⁵.
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Given α = ∆L / L∆T, solve for ∆L
∆L = αL∆T ∆L = 1.2x10⁻⁵ * 200 feet * 50 = 0.12 feet L at 35 = L + ∆L = 200.12 feet |
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Pyrex can withstand large temperature changes because...
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it has a small coefficient of expansion
~4*10⁻⁶ m / m K smaller coefficient of expansion means that it can withstand greater thermal shock |
