Interconversion of Temperature Scales Celsius The world's most common temperature scale is Celsius. Abbreviated C, it is virtually the same as the old centigradescale and therefore has 100 degrees between the melting point and boiling point of water, taken to occur at 0 and 100 degrees, respectively. Kelvin Temperature is a measure of the thermal energy of a system. Thus cooling can proceed only to the point at which all of the thermal energy is removed from the system, and this process defines the temperature of absolute zero. The Kelvin scale, also called the absolute temerature scale, takes its zero to be absolute zero. It uses units of kelvins (abbreviated K), which are the same size as the degrees on the Celsius scale. FahrenheitThis anachronistic temperature scale, used primarily in the United States, has zero defined as the lowest temperature that can be reached with ice and salt, and 100 degrees as the hottest daytime temperature observed in Italy by Torricelli. A. In the equation of state for the perfect gas, , which of the following three temperature scales must be used? Celsius Kelvin Fahrenheit B. What i s the formu la use d to c onver t a te mpera ture in degre es Ce lsius ( ) to t he s ame temper at ur e in ke lvins ( )? Express in terms of .= T_C + 273 orT_C + 273.15 C. What i s the formu la used to c onver t a te mpera ture in degre es Fa hrenh eit ( ) to the same temper at ur e i n degrees Celsius ( )? Express in terms of .= Answer not displaye dD. It is possi ble to get a goo d "feel" fo r the Celsi us sca le because multi ples of 10 ha ve spec ial significance: o : very cold weather; o : water freezes; o : a cool day, so wear a jacket outside; o : room temperature;
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The world's most common temperature scale is Celsius. Abbreviated C, it is virtually the same as the
old centigrade scale and therefore has 100 degrees between the melting point and boiling point ofwater, taken to occur at 0 and 100 degrees, respectively.
Kelvin
Temperature is a measure of the thermal energy of a system. Thus cooling can proceed only to the
point at which all of the thermal energy is removed from the system, and this process defines the
temperature of absolute zero. The Kelvin scale, also called the absolute temerature scale, takes its zero
to be absolute zero. It uses units of kelvins (abbreviated K), which are the same size as the degrees on
the Celsius scale.
Fahrenheit
This anachronistic temperature scale, used primarily in the United States, has zero defined as the
lowest temperature that can be reached with ice and salt, and 100 degrees as the hottest daytime
temperature observed in Italy by Torricelli.
A. In the equation of state for the perfect gas, , which of the following three
temperature scales must be used?
Celsius
Kelvin
Fahrenheit
B. What is the formula used to convert a temperature in degrees Celsius ( ) to the same
temperature in kelvins ( )?
Express in terms of .
=
T_C + 273
or
T_C + 273.15
C. What is the formula used to convert a temperature in degrees Fahrenheit ( ) to the same
temperature in degrees Celsius ( )?
Express in terms of .
= Answer not displayed
D. It is possible to get a good "feel" for the Celsius scale because multiples of 10 have special
A. The first step is to calculate , the effective thermal conductivity of the wall (or ceiling),
allowing for the fact that the beams are actually only wide and are spaced 16 inches
center to center.
Express numerically to two significant figures, in watts per kelvin per meter squared.
= 0.048 (+/- 2%)
B. What is , the total rate of energy loss due to heat conduction for this house?
Round your answer to the nearest 10 W.
= 2160 (+/- 0.4%) W
C. Let us assume that the winter consists of 150 days in which the outside temperature is 0 C.
This will give the typical number of "heating degree days" observed in a winter along thenortheastern US seaboard. (The cumulative number of heating degree days is given daily by
the National Weather Service and is used by oil companies to determine when they should fill
the tanks of their customers.) Given that a gallon (3.4 kg) of oil liberates
when burned, how much oil will be needed to supply the heat lost by
conduction from this house over a winter? Assume that the heating system is 75% efficient.
Give your answer numerically in gallons to two significant figures.
Gallons consumed = 270 (+/- 3%) gallons per winter
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Heat Radiated by a PersonIn this problem you will consider the balance of thermal energy radiated and absorbed by a person.
Assume that the person is wearing only a skimpy bathing suit of negligible area. As a rough
approximation, the area of a human body may be considered to be that of the sides of a cylinder of
length and circumference .
For the Stefan-Boltzmann constant use .
A. If the surface temperature of the skin is taken to be , how much thermal power
does the body described in the introduction radiate?
Take the emissivity to be .
Express the power radiated into the room by the body numerically, rounded to the
Express the rms angular speed in terms of , , , , and other given quantities.
=sqrt(2*k_B*T/(m*d^2))
B. What is the typical angular frequency for a molecule like at room temperature (
)? Assume that for this molecule is . Take the atomic mass of to be
.
Express numerically in hertz, to three significant figures.
= 6.58*10^11 (+/- 0.2%) Hz
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Velocity and Energy Scaling
Hydrogen molecules have a mass of and oxygen molecules have a mass of , where is defined
as an atomic mass unit ( ). Compare a gas of hydrogen molecules to a gas of
oxygen molecules.
A. At what gas temperature would the average translational kinetic energy of a hydrogen
molecule be equal to that of an oxygen molecule in a gas of temperature 300 K?
Express the temperature numerically in kelvins.
= 300 K
B. At what gas temperature would the root-mean-square (rms) speed of a hydrogen
molecule be equal to that of an oxygen molecule in a gas at 300 K?
State your answer numerically, in kelvins, to the nearest integer.
= 19 (+/- 1%) K
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The Ideal Gas Law Derived
The ideal gas law, discovered experimentally, is an equation of state that relates the observable state
variables of the gas—pressure, temperature, and density (or quantity per volume):
(or ),
where is the number of atoms, is the number of moles, and and are ideal gas constants such
that , where is Avogadro's number. In this problem, you should use Boltzmann's
constant instead of the gas constant .
Remarkably, the pressure does not depend on the mass of the gas particles. Why don't heavier gasparticles generate more pressure? This puzzle was explained by making a key assumption about the