course Phy 202
6/29 11:30pI am behind schedule but I have a lot of free time coming up so I will be getting myself back on track very soon. Any feedback on this test will be so helpful because I am finding myself lost on some questions. Thanks!
Problem Number 1
A wall is made of a substance whose thermal conductivity is .97 J / (m sec Celsius). What is the outside temperature of the wall if its thickness is 30 cm and its cross-sectional area 31 m^2, and if thermal energy flows through the wall at a rate of 30 watts when the inside temperature is 22 Celsius?
.The equation for the thermal conductivity of a substance is:
Rate= k*A*(dT/dX) Because we’re looking for T2 I manipulated the equation to be
T2= [(k*A)/rate]*x+ T1
T2=[(.97 J/(m sec C)* 31 m^2)/ 30 watts]* 30 cm +22 C
T2= 52.069 C
The units of the calculation you express are
J / (m sec C) * m^2 / (watts) * cm = J m cm / (sec C J / sec) = m * cm / C.
Your approach is good, but the units don't work out, which should lead you to suspect your algebra.
If
Rate= k*A*(`dT/`dX)
then
`dT = rate * `dX / (k * A), so
T2 - T1 = rate * `dX / (k * A)
If you express `dX in meters, your units will work out.
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Problem Number 2
Analyze the pressure vs. volume of a 'bottle engine' consisting of 4 liters of an ideal gas as it operates between minimum temperature 200 Celsius and maximum temperature 330 Celsius, pumping water to half the maximum possible height. Sketch a pressure vs. volume graph from the original state ato the maximum-temperature state and use the graph to determine the useful work done by the expansion. Then, assuming a monatomic gas, determine the thermal energy required to perform the work and the resulting practical efficiency of the process.
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.The thermal energy required to perform the work is
Thermal energy = 3/2 n *R*dT
TE= (3/2)* (8.32 J/(mole*k))* 130 K
TE= 1620.45 J/mole
This situation is covered in your Class Notes #'s 8 - 10, and is related to the Bottle Engine experiment you were to view.
See if you can apply those ideas to this analysis. Once you have done so, send me your work and I'll be glad to clarify it further.
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Problem Number 3
A certain metal has coefficient of linear expansion 16 * 10^-6 / Celsius. By how much would the volume of a container of this metal with a capacity of 230 liters change if the container was heated from 273 C to 323 C? If the ideal gas in the container was allowed to expand into a balloon, would the increased volume of the balloon be significantly affected by the increased capacity of the container?
To find the change in volume after expansion, we use the equation
dV= beta*Vo*dT
dV= (16*10^-6/C)*(230L)*(323-273)
dV= 0.184 L
I don’t think that the increased volume of the balloon would be significantly affected because the change is not a significantly large one. Therefore I don’t think it would change much.
You're right, but you should in addition figure out how much the gas would expand between these temperatures, and use that result as your basis for comparison.
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Problem Number 4
Water is descending in a vertical pipe of diameter 9 cm and open to the atmosphere. At a lower point the water flows into a smaller pipe of diameter 1.44 cm. At a certain instant the depth of the water just above the narrowing point is 39 cm and the water is moving at 192 cm/s. What is the gauge pressure of the water just above the narrowing point? What is the pressure change across the narrowing point?
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.I’m almost certain that my answer is wrong, but Im not sure how to go about this one.
First I found the difference ratio between the diameters
dD= 1.44/9= 0.16
I can use this to get the velocity at the second diameter
V2= 192*0.16= 30.72
The ratio of velocities depends on the ratio of the cross-sectional areas, not the ratio of the diameters.
Next I used Bernoulli’s equation to find the pressure
P= ½ ‘rho (v2^2-v1^2)
P= ½ (39)*[(30.72^2)-(192^2)]
P= -35,920 L, so the pressure decreases by this amount?
you didn't use units in your calculation; you need to use units with every quantity at every step of your work, and work out the algebra of the units
otherwise, if you make the change suggested earlier, you'll come out OK on this one.
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Problem Number 5
When a sample of .95 kg of a certain material is suspended from a string and immersed in water, the tension in the string is 7.354 Newtons. What is the buoyant force on the sample?
.According to Newton’s second law Fb-T-mg=0
We’re looking for buoyant force so the equation becomes
-Fb= -T-mg which goes to Fb= T+mg
Fb= 7.354 N+ (.95 kg* 9.81)
Fb= 16.6735 N
The net force is zero.
Buoyant force and tension both act upward, the weight mg downward.
Thus the correct relationship is
Fb + T - mg = 0.
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Problem Number 6
A monatomic gas in a 3-liter container is originally at 28 Celsius and atmospheric pressure. It is heated at constant volume until its temperature is 188 Celsius, then at constant pressure until the gas has increased its volume by .68 liters. How much thermal energy is required? By how much does the internal energy of the gas change? How much work is done in the process?
Because the system is confined to a constant volume while the temperature is changing, no thermal energy is required to expand the gas.
good; this is the case for the first phase of the expansion
The amount of work done can be found by
W= (25 J/mol*k)* dT
W= (25 J/mol*k)* 160 K
W= 4000 J
note that there's a second phase, the constant-pressure expansion
What temperature will be required to complete that expansion?
How much thermal energy will be required?
etc.
As far as internal energy, I know that we will have a value for this because the temperature of the gas changes. But I could not figure out how to come to this value with out knowing the number of moles. HELP!!
you have the initial volume, temperature and pressure, so you can use the gas law to find the number of moles