Concept explainers
Each year thousands of children are badly burned by hot tap water. Figure P16.11 shows a cross-sectional view of an antiscalding faucet attachment designed to prevent such accidents. Within the device, a spring made of material with a high coefficient of thermal expansion controls a movable plunger. When the water temperature rises above a preset safe value, the expansion of the spring causes the plunger to shut off the water flow. Assuming that the initial length L of the unstressed spring is 2.40 cm and its coefficient of linear expansion is 22.0 × 10–6 (°C)–1, determine the increase in length of the spring when the water temperature rises by 30.0°C. (You will find the increase in length to be small. Therefore, to provide a greater variation in valve opening for the temperature change anticipated, actual devices have a more complicated mechanical design.)
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Principles of Physics: A Calculus-Based Text
- A gas is in a container of volume V0 at pressure P0. It is being pumped out of the container by a piston pump. Each stroke of the piston removes a volume Vs through valve A and then pushes the air out through valve B as shown in Figure P19.74. Derive an expression that relates the pressure Pn of the remaining gas to the number of strokes n that have been applied to the container. FIGURE P19.74arrow_forwardWater at 15°C is to be pumped from a reservoir (zA = 2 m) to another reservoir at a higher elevation (zB = 9 m) through two 25-m-long plastic pipes connected in parallel. The diameters of the two pipes are 3 cm and 5 cm. Water is to be pumped by a 68 percent efficient motor–pump unit that draws 8 kW of electric power during operation. The minor losses and the head loss in the pipes that connect the parallel pipes to the two reservoirs are considered to be negligible. Determine the total flow rate between the reservoirs and the flow rates through each of the parallel pipes.arrow_forwardDuring inhalation, a person's diaphragm and intercostal muscles contract, expanding the chest cavity and lowering the internal air pressure below ambient so that air flows in through the mouth and nose to the lungs. Suppose a person's lungs hold 1220 mL of air at a pressure of 1.00 atm. If they expand their chest cavity by 530 mL while keeping their nose and mouth closed so that no air is inhaled, what will be the air pressure in their lungs in atm? Assume the air temperature remains constant. HINT atm Need Help? Read It Watch Itarrow_forward
- During inhalation, a person's diaphragm and intercostal muscles contract, expanding the chest cavity and lowering the internal air pressure below ambient so that air flows in through the mouth and nose to the lungs. Suppose a person's lungs hold 1240 mL of air at a pressure of 1.00 atm. If they expand their chest cavity by 515 mL while keeping their nose and mouth closed so that no air is inhaled, what will be the air pressure in their lungs in atm? Assume the air temperature remains constant.arrow_forwardA vacuum pump is used to drain the flooded mine shaft of 20 degrees Celcius water. The pump pressure of water at this temperature is 2.34 Kpa. The pump is incapable of lifting the water higher than 10.16 m. What is the atmospheric pressure?arrow_forwardYou are inflating the tires on your bicycle using a manual pump. The volume inside of the pump is initially 0.16 m cube with a pressure of 2 atm. If you push down on the piston and reduce the volume inside to 0.07 m cube, what is the new pressure inside of the pump? Assume the temperature inside the pump stays constant.arrow_forward
- A liquid with a coefficient of volume expansion of β just fills a spherical flask of volume V 0 at temperature Ti (Fig. P10.57). The flask is made of a material that has a coefficient of linear expansion of a. The liquid is free to expand into a capillary of cross- sectional area A at the top. (a) Show that if the temperature increases by ΔT, the liquid rises in the capillary by the amount Δh = (V0 /A)(β − 3α)ΔT. (b) For a typical system, such as a mercury thermometer, why is it a good approximation to neglect the expansion of the flask?arrow_forwardA pressure versus volume (pv) diagram for a system is shown in the figure. The arrows of the curve indicate the direction of the process, and the points of interest are labeled. The values for the points in the diagram are shown in the table. Volume (m3) Pressure (Pa) v0=27.4 p0=1.00×104 v1=19.3 p1=1.00×104 v2=16.0 p2=4.92×103 v3=13.3 p3=4.92×103 v4=13.3 p4=3.20×103 v5=7.51 p5=1.00×103 Calculate the amount of work done on the system from 0–2 (W02) and then for the entire curve from 0–5 (W05).arrow_forwardA pressure versus volume (pV) diagram for a system is shown in the figure. The arrows of the curve indicate the direction of the process, and the points of interest are labeled. The values 1 for the points in the diagram are shown in the table. Volume (m³) Pressure (Pa) Vo 25.8 Po = 1.00 x 104 3 Vi = 20.8 Pi = 1.00 × 104 V2 = 17.4 P2 5.34 x 103 V3 = 13.9 P3 5.34 x 103 V4 13.9 P4 3.20 x 103 5 Vs = 9.55 P5 = 1.00 x 103 Calculate the amount of work done on the system from 0-2 ( Wo2) and then for the entire curve from 0-5 (Wos). Volume (m³) -6.03 x104 Wo2 = J Incorrect -7.86 x104 Wo5 = J Incorrect Pressure (Pa)arrow_forward
- A cylinder with a cross-sectional area of 0.035 m2 is fitted with a piston that is free to move up and down. The piston has a weight of 14.0 N. The uninsulated cylinder is sitting in a water bath with a temperature of 16◦C. Inside the cylinder is a gas, occupying a volume of 3.6×10−4 cubic meters. (a) What is the initial pressure inside the cylinder? (b) The piston is locked in place and the cylinder is moved to a water bath with a temperature of 70 ◦C. What will be the volume of the gas? What will be the pressure in the gas when it reaches thermal equilibrium with the hot water bath? What kind of a change is this? Isothermal, isobaric, isovolumetric, or adiabatic? (c) A weight of 15.5 N is placed on top of the piston and then the piston is unlocked so that it is free to move again. What will be the pressure in the gas when the piston is in equilibrium? What will be the volume of the gas when the pistion is in equilibrium? What kind of a change is this? Isothermal, isobaric,…arrow_forwardA pressure versus volume (pV) diagram for a system is shown in the figure. The arrows of the curve indicate the direction of the process, and the points of interest are labeled. The values for the points in the diagram are shown in the table. Volume (m³) Pressure (Pa) Vo = 25.8 Po = 1.00 × 10ª %3D 2 3 Vị = 20.8 Рі 3D 1.00 х 104 V2 = 17.4 P2 = 5.34 × 103 V3 13.9 P3 = 5.34 x 103 4 V4 = 13.9 P4 = 3.20 × 10³ %3| Vs = 9.55 P5 = 1.00 x 103 %3D Calculate the amount of work done on the system from 0–2 ( Wo2) and then for the entire curve from 0-5 (Wo5). Volume (m³) 79.81 x103 Wo2 J Incorrect 107.09 x103 Wo5 J Incorrect Pressure (Pa)arrow_forwardhigh-pressure gas cylinder contains 50.0 L of toxic gas at a pressure of 1.35 × 107 Pa and a temperature of 25.0°C. Its valve leaks after the cylinder is dropped. The cylinder is cooled to dry ice temperature (-78.5°C) to reduce the leak rate and pressure so that it can be safely repaired. A) what is the final pressure, in pascals, in the tank assuming negligible amount of gas leaks while being cooled and that there is no phase change ? B) What is the final pressure in pascals if one tenth of the gas escapes during the process? C) to what tempature in kelvins must tank be cooled from inital state to reduce the pressure to 1.00 atm (assuming the gas does not change phase and there is no leakage during cooling)?arrow_forward
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