course Phy 202
I am having trouble finding the efficiency. I am dividing the work done/by thermal energy and I keep getting 1 for all of them. So I know that isn't correct. Also, I am having trouble finding the new temp. Any help would be appreciated.
See my notes and see if you can answer my questions. Be sure to include my questions with your revision and with your answers.
Let me know if anything is unclear, and include specifics about what you do and do not understand.
I am having trouble finding the efficiency. I am dividing the work done/by thermal energy and I keep getting 1 for all of them. So I know that isn't correct. Also, I am having trouble finding the new temp. Any help would be appreciated.
1. Determine the amount of work done by the system (the amount of work done is equal to the increase in the potential energy of the water). Figuring the weight of water raised and multiplying it by the height to which it is raised gives the work done. For example at 80 cm height the 105 ml of water raised has a mass of 105 grams or .105 kg, so the weight is .105 kg * 9.8 m/s^2 = 1.029 Newton. Raising 1.029 Newton a distance of .8 meters results in work 1.029 N * .8 m = .8232 Joules, approx.
Height water raised Mass of water Weight of water Work
.2 m .18 kg 1.764 N .3528 J
.53 m .135 kg 1.323 N .70119 J
.8 m .105 kg 1.029 N .8232 J
1 m .05 kg .49 N .49 J
1.2 m .03 kg .294 N .3528 J
2. Determine the pressure in the bottle as water is flowing out the top of the tube (Bernoulli's Equation applies--the pressure of the water flowing out of the tube is atmospheric pressure, about 100 kPa; the altitude of the water is less at the water surface in the bottle than at the top of the tube). For example: P = `rho g y=1000 kg / m^3 * 9.8 m/s^2 * .2 meters = 1960 N/m^2.
Height Pressure
.2 M 1960 N/m^2
.53 M 5194 N/m^2
.8 M 7840 N/m^2
1 M 9800 N/m^2
1.2 M 11760 N/m^2
These are the correct pressure difference between the top of the tube and the bottom.
However the pressure at the top of the tube is atmospheric pressure. So you have to add these pressures to atmospheric pressure to get the pressure in the bottle.
3. Determine the temperature in the bottle, assuming that the inside temperature was 7 Celsius when the bottle was sealed off from the atmosphere.
When the bottle was sealed off from the atmosphere, before heating, the pressure was 1 atmosphere and the temperature was 7 Celsius.
The volume of the bottle doesn't change significantly and no gas enters or leaves.
You know the pressure at each height (as soon as you have added atmospheric pressure to your above results).
So what is the temperature at each height.
4. If the air in the bottle requires 5/2 * 8.31 J / mole to raise its temperature by 1 degree Kelvin, then how much thermal energy did it take to heat the air? Expanding the gas requires energy P * `dV; at the 80 cm height the gas expands by 105 ml = .105 liters and pressure is about 7840 N/m^2, which indicates a thermal energy transfer of P `dv = .105*10-3m^3* 7840 N/m^2 = .8232 Joules
Height Thermal Energy Transfer
.2 M .3528 Joules
.53 M .70119 Joules
.8 M .8232 Joules
1 M .49 Joules
1.2 M .3528 Joules
You need to figure out the energy required to heat the gas. The results you give here are only the PE changes. Very much more energy that that is required to heat the gas.
How many moles of gas were in the container?
By how much did the temperature change while water was rising in the tube?
How much thermal energy change was required?
By how much did the temperature change while water was flowing out of the tube?
How much thermal energy change was required?
Your answers on the remaining questions will need to be modified accordingly.
5. What is the efficiency of the process, defined as the work done divided by the thermal energy supplied to the system?
Height Efficiency
.2 M
.53 M
.8 M
1 M
1.2 M
6. Why does the system not do as much work when the height to which water is raised is too small?
Since pressure in the open end of the tube remains at atmospheric pressure, the water must rise in the tube to equalize pressures within the bottle. We note that until the water reaches the top of the tube there is very little expansion of the air inside the bottle--since the tube has very little volume very little fluid must be displaced to fill the tube.
7. Why does the system not do as much work when the height to which water is raised is too great?
This is the greatest possible height and the weight of the water is less at this point which results in a lesser work.
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