# 13.2 Thermal expansion of solids and liquids  (Page 6/10)

 Page 6 / 10

Does it really help to run hot water over a tight metal lid on a glass jar before trying to open it? Explain your answer.

Liquids and solids expand with increasing temperature, because the kinetic energy of a body’s atoms and molecules increases. Explain why some materials shrink with increasing temperature.

## Problems&Exercises

The height of the Washington Monument is measured to be 170 m on a day when the temperature is $\text{35}\text{.}0\text{º}\text{C}$ . What will its height be on a day when the temperature falls to $–\text{10}\text{.}0\text{º}\text{C}$ ? Although the monument is made of limestone, assume that its thermal coefficient of expansion is the same as marble’s.

169.98 m

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

What is the change in length of a 3.00-cm-long column of mercury if its temperature changes from $\text{37}\text{.}0\text{º}\text{C}$ to $\text{40}\text{.}0\text{º}\text{C}$ , assuming the mercury is unconstrained?

$5\text{.}4×{\text{10}}^{-6}\phantom{\rule{0.25em}{0ex}}\text{m}$

How large an expansion gap should be left between steel railroad rails if they may reach a maximum temperature $\text{35}\text{.}0\text{º}\text{C}$ greater than when they were laid? Their original length is 10.0 m.

You are looking to purchase a small piece of land in Hong Kong. The price is “only” \$60,000 per square meter! The land title says the dimensions are $\text{20}\phantom{\rule{0.25em}{0ex}}\text{m}\phantom{\rule{0.20em}{0ex}}×\phantom{\rule{0.20em}{0ex}}\text{30 m}\text{.}$ 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 $\text{20}\text{º}\text{C}$ above normal?

Because the area gets smaller, the price of the land DECREASES by $\text{~}\text{17},\text{000}\text{.}$

Global warming will produce rising sea levels partly due to melting ice caps but also 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 $1\text{.}\text{00}\text{º}\text{C}\text{.}$ Note that this calculation is only approximate because ocean warming is not uniform with depth.

Show that 60.0 L of gasoline originally at $\text{15}\text{.}0\text{º}\text{C}$ will expand to 61.1 L when it warms to $\text{35}\text{.}0\text{º}\text{C,}$ as claimed in [link] .

$\begin{array}{lll}V& =& {V}_{0}+\text{Δ}V={V}_{0}\left(1+\beta \text{Δ}T\right)\\ & =& \left(\text{60}\text{.}\text{00 L}\right)\left[1+\left(\text{950}×{\text{10}}^{-6}/\text{º}\text{C}\right)\left(\text{35}\text{.}0\text{º}\text{C}-\text{15}\text{.}0\text{º}\text{C}\right)\right]\\ & =& \text{61}\text{.}1\phantom{\rule{0.25em}{0ex}}\text{L}\end{array}$

(a) Suppose a meter stick made of steel and one made of invar (an alloy of iron and nickel) are the same length at $0\text{º}\text{C}$ . What is their difference in length at $\text{22}\text{.}0\text{º}\text{C}$ ? (b) Repeat the calculation for two 30.0-m-long surveyor’s tapes.

(a) If a 500-mL glass beaker is filled to the brim with ethyl alcohol at a temperature of $5\text{.}\text{00}\text{º}\text{C,}$ how much will overflow when its temperature reaches $\text{22}\text{.}0\text{º}\text{C}$ ? (b) How much less water would overflow under the same conditions?

(a) 9.35 mL

(b) 7.56 mL

Most automobiles 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 $\text{10}\text{.}0º\text{C}\text{.}$ What volume of radiator fluid will overflow when the radiator and fluid reach their $\text{95}\text{.}0º\text{C}$ operating temperature, given that the fluid’s volume coefficient of expansion is $\beta =\text{400}×{\text{10}}^{–6}/\text{º}\text{C}$ ? Note that this coefficient is approximate, because most car radiators have operating temperatures of greater than $\text{95}\text{.}0\text{º}\text{C}\text{.}$

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 $\text{350}\phantom{\rule{0.25em}{0ex}}{\text{cm}}^{3}$ of coffee is in a 7.00-cm-diameter cup and decreases in temperature from $\text{95}\text{.}0\text{º}\text{C}\phantom{\rule{0.25em}{0ex}}$ to $\phantom{\rule{0.25em}{0ex}}\text{45}\text{.}0\text{º}\text{C}\text{.}$ (Most of the drop in level is actually due to escaping bubbles of air.)

0.832 mm

(a) The density of water at $0\text{º}\text{C}$ is very nearly $\text{1000}\phantom{\rule{0.25em}{0ex}}{\text{kg/m}}^{3}$ (it is actually $9\text{99}\text{.}{\text{84 kg/m}}^{3}$ ), whereas the density of ice at $0\text{º}\text{C}$ is $9{\text{17 kg/m}}^{3}$ . 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.) (b) What are the implications of this result for biological cells that are frozen?

Show that $\beta \approx 3\alpha ,$ by calculating the change in volume $\text{Δ}V$ of a cube with sides of length $L\text{.}$

We know how the length changes with temperature: $\text{Δ}L={\mathrm{\alpha L}}_{0}\text{Δ}T$ . Also we know that the volume of a cube is related to its length by $V={L}^{3}$ , so the final volume is then $V={V}_{0}+\text{Δ}V={\left({L}_{0}+\text{Δ}L\right)}^{3}$ . Substituting for $\text{Δ}L$ gives

$V={\left({L}_{0}+{\mathrm{\alpha L}}_{0}\text{Δ}T\right)}^{3}={L}_{0}^{3}{\left(1+\alpha \text{Δ}T\right)}^{3}\text{.}$

Now, because $\alpha \text{Δ}T$ is small, we can use the binomial expansion:

$V\approx {L}_{0}^{3}\left(1+3\alpha \Delta T\right)={L}_{0}^{3}+3\alpha {L}_{0}^{3}\text{Δ}T.$

So writing the length terms in terms of volumes gives $V={V}_{0}+\text{Δ}V\approx {V}_{0}+{3\alpha V}_{0}\text{Δ}T,$ and so

$\text{Δ}V={\mathrm{\beta V}}_{0}\text{Δ}T\approx {3\alpha V}_{0}\text{Δ}T,\phantom{\rule{0.25em}{0ex}}\text{or}\phantom{\rule{0.25em}{0ex}}\beta \approx 3\alpha .$

An American traveler in New Zealand carries a transformer to convert New Zealand’s standard 240 V to 120 V so that she can use some small appliances on her trip.
What is the ratio of turns in the primary and secondary coils of her transformer?
nkombo
How electric lines and equipotential surface are mutually perpendicular?
The potential difference between any two points on the surface is zero that implies È.Ŕ=0, Where R is the distance between two different points &E= Electric field intensity. From which we have cos þ =0, where þ is the angle between the directions of field and distance line, as E andR are zero. Thus
sorry..E and R are non zero...
By how much leeway (both percentage and mass) would you have in the selection of the mass of the object in the previous problem if you did not wish the new period to be greater than 2.01 s or less than 1.99 s?
what Is linear momentum
why no diagrams
where
Fayyaz
Myanmar
Pyae
hi
Iroko
hello
Abdu
Describe an experiment to determine short half life
what is science
it's a natural phenomena
Hassan
sap
Emmanuel
please can someone help me with explanations of wave
Benedine
A 20MH coil has a resistance of 50 ohms and us connected in series with a capacitor to a 520MV supply
what is physics
it is the science which we used in our daily life
Sujitha
Physics is the branch of science that deals with the study of matter and the interactions it undergoes with energy
Junior
it is branch of science which deals with study of happening in the human life
AMIT
A 20MH coil has a resistance of 50 ohms and is connected in series with a capacitor to a 250MV supply if the circuit is to resonate at 100KHZ, Determine 1: the capacitance of the capacitor 2: the working voltage of the circuit, given that pie =3.142
Musa
Physics is the branch of science that deals with the study of matter and the interactions it undergoes with energy
Kelly
Heat is transfered by thermal contact but if it is transfered by conduction or radiation, is it possible to reach in thermal equilibrium?
Yes, It is possible by conduction if Surface is Adiabatic
Astronomy
Yeah true ilwith d help of Adiabatic
Kelly
what are the fundamentals qualities
what is physic3
Kalilu
what is physic
Kalilu
Physics? Is a branch of science dealing with matter in relation to energy.
Moses
Physic... Is a purging medicine, which stimulates evacuation of the bowels.
Moses
are you asking for qualities or quantities?
Noman
give examples of three dimensional frame of reference
Universe
Noman
Yes the Universe itself
Astronomy
Examine different types of shoes, including sports shoes and thongs. In terms of physics, why are the bottom surfaces designed as they are? What differences will dry and wet conditions make for these surfaces?
sports shoes are designed in such a way they are gripped well with your feet and their bases have and high friction surfaces, Thong shoes are for comfort, these are easily removed and light weight. these are usually low friction surfaces but in wet conditions they offer greater friction.
Noman
thong sleepers are usually used in restrooms.
Noman
what is wave
The phenomenon of transfer of energy
Noman
how does time flow in one dimension
yeah that was a mistake
Lord
if it flows in three dimensions does it mean if an object theoretically moves beyond the speed of light it won't experience time
Lord
but if an object moves beyond the speed of light time stops right for it
Lord
yes but at light speed it ceases
Lord
yes it always flow from past to future.
Noman