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course phy 232
Here is what i have for this lab so far. I feel the questions later on all depend on my answers for these first few questions and I want to make sure I get those right. The directions say to NOT have the PE change in terms of y, but how can I do that?
@& It's in terms of the intermediate temperature T.*@
Ph2 110209`q001. The same process we modeled in class last time has the following characteristics:
The temperatures of the hot and cold sources are T_c and T_h, initial volume is V_0, initial pressure is P_0, water density is rho and the acceleration of gravity is g.
The system is heated at constant volume, starting at T = T_c, until the temperature is T, where T_c < T < T_h, raising water in a thin tube whose end is open to the atmosphere.
The system is allowed to expand at constant pressure until it comes to final temperature T = T_h, displacing water as it expands. The water exits from the end of the tube.
The system is then cooled to its original temperature and pressure, without doing additional work or absorbing more thermal energy from the hot source.
In terms of T_c, T_h, V_0, P_0, rho and g
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How much PE does the system gain in the process?
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PE gained is rho*g*y*(V0(Th/Tc)(P0/(rho*g*y+P0))-V0).....from the previous lab
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Assuming the gas to be diatomic, how much thermal energy flows into the system during the process?
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(5/2)nr(Th/((P0+rho*g*y)/P0)-Th)+(7/2)nR(Tc-(Th/((P0+rho*g*y)/P0)))....again, from the previous lab
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What therefore is the ratio of PE gain to thermal energy absorbed by the system?
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[rho*g*y*(V0(Th/Tc)(P0/(rho*g*y+P0))-V0)]/[(5/2)nr(Th/((P0+rho*g*y)/P0)-Th)+(7/2)nR(Tc-(Th/((P0+rho*g*y)/P0)))]
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How would your answer differ if the gas was monatomic, and why?
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the thermal energy factor would decrease. There wouldn't be any rotational KE, so I would have:
(3/2)nr(Th/((P0+rho*g*y)/P0)-Th)+(5/2)nR(Tc-(Th/((P0+rho*g*y)/P0)))
@& y is not a given parameter in this question, T is.
If T is the intermediate temperature, then P_0 + rho g y = P_0 * (T / T_c).
Note that I should have listed T among the quantities in terms of which the result should be expressed, so the linst would be T_c, T_h, T, V_0, P_0, rho and g.
Also I think in the notes I used T_i for this intermediate temperature, rather that T (which could be confusing).*@
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`q002. By heating the air in a bottle from 273 K to 300 K, you have raised water in a thin vertical tube to a height of about 100 cm.
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By how much will the water level in the tube change, per Kelvin, if the temperature is changed?
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that would be (change in height)/(change in temperature), so I get 3.7 cm per degree Kelvin.
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Assume the tube has cross-sectional area 0.1 cm^2. This could make a small difference in your preceding answer, which was based on the assumption that the volume of the tube is negligible. We won't worry about that for the preceding, but we will need to consider it for the following.
However the cross-sectional area of the tube makes a difference to the following:
If the tube makes a sharp right-angle turn at the 100 cm height (becoming horizontal), then how many cm of the additional tube will be filled, per Kelvin, if the temperature increases?
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Would the our results change if the air in the bottle had initially been at 290 Kelvin (assume that the water level and the position at which the tube makes its right-angle turn are adjusted accordingly)?
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What would change in our analysis if instead of a right-angle turn, the angle changed by a little less than 90 degrees, so that the tube has an upward slope of 0.1?
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`q003. A wall is constructed of two different materials of equal thickness, the first with double the thermal conductivity of the other. The inner and outer walls are maintained at a constant temperature difference until a steady flow of thermal energy through the wall is achieved.
At that time, which wall will have the greater temperature gradient, and what will be the ratio of the temperature gradients? Hint: In the steady state, equal amounts of thermal energy pass through both materials.
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What therefore is the ratio of the temperature change through the first layer, to the temperature change through the second?
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If the inner wall is at temperature 30 Celsius and the outer at temperature 10 Celsius, what is the temperature at the point where the layers meet?
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If the first wall is also 50% thick than the other, how will the steady-state temperature gradients compare?
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What therefore is the ratio of the temperature change through the first layer, to the temperature change through the second?
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If the inner wall is at temperature 30 Celsius and the outer at temperature 10 Celsius, what is the temperature at the point where the layers meet?
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`q004. (University Physics) The PE gain of the system analyzed in the previous class is V0 ( (T_h / T_c) * ( P_0 / (P_0 + rho g y) ) - 1) ) * rho g y.
If the system is heated from temperature T_c to temperature T_h, at constant volume, what will be the maximum pressure and what therefore will be the maximum possible value of y?
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Substitute this maximum possible value of y for into the equation and simplify. What is your result, and why does this result make sense?
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If the system is heated from temperature T_c to temperature T_h, at the constant initial pressure P_0, then how much water will be displaced, and to what height y? How much PE change will therefore occur?
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We can factor all constant factors from the rest of the expression, obtaining the form
`dPE = rho g V0 * ( (T_h / T_c) * ( P_0 / (P_0 + rho g y) ) - 1) ) * y.
Find the value of y at which this expression is maximized.
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Find the value of `dPE for this maximizing value of y.
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Sketch a graph of `dPE vs. y.
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`q005. The system first analyzed in the preceding class had a rectangular P vs. V graph, due to the way the system was first cooled until it reached the original pressure.
The third phase of the cycle changes if we allow the gas to expand suddenly. Instead of a vertical line segment we get a part of the adiabatic curve P V^gamma = constant. This results in a different initial temperature T_3 and a different initial volume V_3 for the fourth phase of the cycle (that phase is still isobaric, just over a different range of volumes).
What will be the expressions for T_3 and V_3?
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The PE change of the system remains the same as before. However the work done by the system does differ from our previous result? What is the expression for the work done by this system?
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How does the amount of thermal energy transferred to the cold sink differ between the original cycle and this one?
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`q006. The third phase of the cycle could also be accomplished isothermally, adding thermal energy to the (more slowly) expanding gas until it reaches the original temperature. Since T and n remain constant, the graph will in this case follow an isothermal curve P V = constant. Again T_3 and V_3 will differ from the values obtained for previous cycles, as will the amount of energy absorbed from the hot sink and the amount absorbed by the cold sink.
What will be the expressions for T_3 and V_3?
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What is the expression for the work done by this system?
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How does the amount of thermal energy transferred to the cold sink differ between the original cycle and this one?
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How does the amount of thermal energy absorbed from the hot sink differ between the original cycle and this one?
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@& See if my note clarifies the situation.*@