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How much taller does the Eiffel Tower become at the end of a day when the temperature has increased by 15 ° C? Its original height is 321 m and you can assume it is made of steel.

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What is the change in length of a 3.00-cm-long column of mercury if its temperature changes from 37.0 ° C to 40.0 ° C , assuming the mercury is constrained to a cylinder but unconstrained in length? Your answer will show why thermometers contain bulbs at the bottom instead of simple columns of liquid.

Using [link] to find the coefficient of thermal expansion of mercury:
Δ L = α L Δ T = ( 6.0 × 10 −5 / ° C ) ( 0.0300 m ) ( 3.00 ° C ) = 5.4 × 10 −6 m .

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How large an expansion gap should be left between steel railroad rails if they may reach a maximum temperature 35.0 ° C greater than when they were laid? Their original length is 10.0 m.

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You are looking to buy a small piece of land in Hong Kong. The price is “only” $60,000 per square meter. The land title says the dimensions are 20 m × 30 m . By how much would the total price change if you measured the parcel with a steel tape measure on a day when the temperature was 20 ° C above the temperature that the tape measure was designed for? The dimensions of the land do not change.

On the warmer day, our tape measure will expand linearly. Therefore, each measured dimension will be smaller than the actual dimension of the land. Calling these measured dimensions l ' and w ' , we will find a new area, A . Let’s calculate these measured dimensions:
l ' = l 0 Δ l = ( 20 m ) ( 20 ° C ) ( 20 m ) ( 1.2 × 10 −5 ° C ) = 19.9952 m ;
A ' = l × w ' = ( 29.9928 m ) ( 19.9952 m ) = 599.71 m 2 ;
Cost change = ( A A ' ) ( $ 60,000 m 2 ) = ( ( 600 599.71 ) m 2 ) ( $ 60,000 m 2 ) = $ 17,000 .
Because the area gets smaller, the price of the land decreases by about $17,000.

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Global warming will produce rising sea levels partly due to melting ice caps and partly due to the expansion of water as average ocean temperatures rise. To get some idea of the size of this effect, calculate the change in length of a column of water 1.00 km high for a temperature increase of 1.00 ° C . Assume the column is not free to expand sideways. As a model of the ocean, that is a reasonable approximation, as only parts of the ocean very close to the surface can expand sideways onto land, and only to a limited degree. As another approximation, neglect the fact that ocean warming is not uniform with depth.

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(a) Suppose a meter stick made of steel and one made of aluminum are the same length at 0 ° C . What is their difference in length at 22.0 ° C ? (b) Repeat the calculation for two 30.0-m-long surveyor’s tapes.

a. Use [link] to find the coefficients of thermal expansion of steel and aluminum. Then Δ L Al Δ L steel = ( α Al α steel ) L 0 Δ T = ( 2.5 × 10 −5 ° C 1.2 × 10 −5 ° C ) ( 1.00 m ) ( 22 ° C ) = 2.9 × 10 −4 m .
b. By the same method with L 0 = 30.0 m , we have Δ L = 8.6 × 10 −3 m .

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(a) If a 500-mL glass beaker is filled to the brim with ethyl alcohol at a temperature of 5.00 ° C , how much will overflow when the alcohol’s temperature reaches the room temperature of 22.0 ° C ? (b) How much less water would overflow under the same conditions?

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Most cars have a coolant reservoir to catch radiator fluid that may overflow when the engine is hot. A radiator is made of copper and is filled to its 16.0-L capacity when at 10.0 ° C . What volume of radiator fluid will overflow when the radiator and fluid reach a temperature of 95.0 ° C, given that the fluid’s volume coefficient of expansion is β = 400 × 10 −6 / ° C ? (Your answer will be a conservative estimate, as most car radiators have operating temperatures greater than 95.0 ° C ).

Δ V = 0.475 L

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A physicist makes a cup of instant coffee and notices that, as the coffee cools, its level drops 3.00 mm in the glass cup. Show that this decrease cannot be due to thermal contraction by calculating the decrease in level if the 350 cm 3 of coffee is in a 7.00-cm-diameter cup and decreases in temperature from 95.0 ° C to 45.0 ° C . (Most of the drop in level is actually due to escaping bubbles of air.)

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The density of water at 0 ° C is very nearly 1000 kg/m 3 (it is actually 999.84 kg/m 3 ), whereas the density of ice at 0 ° C is 917 kg/m 3 . Calculate the pressure necessary to keep ice from expanding when it freezes, neglecting the effect such a large pressure would have on the freezing temperature. (This problem gives you only an indication of how large the forces associated with freezing water might be.)

If we start with the freezing of water, then it would expand to ( 1 m 3 ) ( 1000 kg/m 3 917 kg/m 3 ) = 1.09 m 3 = 1.98 × 10 8 N/m 2 of ice.

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Show that β = 3 α , by calculating the infinitesimal change in volume dV of a cube with sides of length L when the temperature changes by dT .

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Questions & Answers

Newton's second laws is call with
Dyutee Reply
Really
Arzoodan
what is mean by thermodynamics
Prasad Reply
it is study about temperature and it's equilibrium
thiru
Its the study of heat and its relation with others kind of energy
Antonio
state caulombs law clearly
constand Reply
show mathematically that an electron has the greater speed than the proton when they attract each other
ezra Reply
show mathematically that an electron has the greater speed than the proton when they attract each other
srikanta
@ezra & srikanta; for electrons: a=ke^2/(mr^2) and for protons: a=kp^2/(mr^2)
Sikandar
what is electrostatics
Hero Reply
the study of charge at rest
Gulzar
@Hero; the study of charges at rest is the electrostatics
Sikandar
okay what is electrostatic?
Abd
charge at rest
Nawal
set of character...
Arzoodan
oky
Abd
Gauss law, electric fields, dipoles,...
Antonio
good
Abd
A proton initially at rest falls through a p.d of 25000V. what speed does it gain?
Minister Reply
@Minister; use equation v= sq root(2×eV/m)
Sikandar
what is the reaction of heat on magnet
ORIZINO Reply
Magnetization decreases with increase in temperature. But in case of diamagnetic substance heat has no role on magnetization.
srikanta
what is a physical significant of electric dipole moment .
PRANAB Reply
A dipole moment it's a mechanical electrical effect used in nature
Antonio
what is the uses of carbon brushes in generator
Malik Reply
to minimize heat
constand
at what temperature is the degree Fahrenheit equal to degree Celsius
Grace Reply
Celsius and Faharaneith are different, never equal
Antonio
find their liners express of n=a+b/T² ( plot graph n against T)
Donsmart Reply
Radio Stations often advertis "instant news,,if that meens you can hear the news the instant the radio announcer speaks it is the claim true? what approximate time interval is required for a message to travel from Cairo to Aswan by radio waves (500km) (Assume the waves Casbe detected at this range )
mahmod Reply
what is growth and decay
Pawan Reply
Can someone please predict the trajectory of a point charge in a uniform electric field????
erlinda Reply
what is deference between strong force and coulomb force
zahid Reply
how do you convert temperature in degree Celsius to Fahrenheit
kwame
Celsius x 9/5 +32
Cyclone
Practice Key Terms 4

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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