A mountain hiker tightens the cap on a half-full plastic water bottle at a high altitude. The volume of air in the sealed bottle is 5 x 10** m°, the pressure is 64 kPa and the temperature is-8°C. The hiker descends to a lower altitude where the pressure is 94.2 kPa and the temperature is 11 °C. -43 What is the final volume of the sealed air inside the bottle? (this is what causes the plastic bottle to deform if you've ever experience this situation)
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![A mountain hiker tightens the cap on a half-full plastic water bottle at a high altitude. The
volume of air in the sealed bottle is 5 x 104 m°, the pressure is 64 kPa and the
temperature is -8 °C. The hiker descends to a lower altitude where the pressure is 94.2
kPa and the temperature is 11 °C.
What is the final volume of the sealed air inside the bottle? (this is what causes the plastic
bottle to deform if you've ever experience this situation)
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- Incandescent lightbulbs are filled with an inert gas to lengthen the filament life. With the current off ( at T = 20.0 degrees Celsius ), the gas inside a lightbulb has a pressure of 113 kPa. When the bulb is burning, the temperature rises to 89.4 degrees Celsius. What is the pressure at the higher temperature?Step 1 (a) The ideal-gas equation describes each condition of the air in the tire. We will set up ratios in order to describe these changes. Dividing the equations PV = nRT in the initial and final states, we have PfVf Tf P¡Vi Ti Solving for the final pressure in the tire, gives Pf = = = which gives I Tf P(V)() P₁ Vf T₁ = (1.013 x 105 Pa) x 105 Pa. Note that the volume V¡ cancels out of the equation. = Vf Po = Pr (V ( ) ( ) Pd Pf Vi V₁ Step 2 (b) After the car is driven, the temperature and volume of air in the tire have changed. Let Td be the temperature and Vd be the volume of air in the tire. We have PdVd Td PfVf Tf' x 105 Pa 273 + 273 + Vf Vf Again we see that the volume Vf cancels out of the equation. °C K °℃ K = x 105 Pa.You happen to come across a piece of metal that has a density of p = 7.43 g/cm³ when the temperature is To = 45.0 °C. If the metal is cooled to a temperature of T = 0.00 °C, does the density change? No, because as the volume changes so does the mass. No, density does not depend on temperature. Yes, since the metal contracts and the mass is constant, the density will increase. Yes, the density will decrease since the volume changes. Calculate the density of the piece of metal at this temperature, p1. The coefficient of volume expansion for this piece of metal is ß = 8.43 x 10-s 1°°C.
- A cylindrical glass flask with a diameter of 8 cm and the height of 20 cm is fully filled with water at 20°C. When the temperature of the water (and consequently the inner surface of the flask) is raised to 100° C, determine the volume of the water that overflows? HINT 1: Don't forget to calculate the initial volume of the water and flask HINT 2: The volume expansion coefficient for ordinary glass and water can be found in the table of Week 4 (Slide #20). HINT 3: Calculate the volume expansions for both water and the flask HINT 4: The difference between the final volume of water and the final volume of the flask is the amount of overflow. PLEASE UPLOAD YOUR HANDWRITTEN SOLUTION BY CLICKING ON THE "ADD A FILE" BUTTON.Suppose you have a large hot air balloon, open at the bottom but filled with air that is heated to 50 °C while the outside air is 10 °C. What can you say about the air inside the balloon and how much it can lift? The density of air is surprisingly high: 1.23 kg/m3, an average hot air balloon has a volume of 3000 m3 , and the acceleration of gravity is 9.8 m/s2. The density is higher by the factor (273 + 50)/(273+10) = 1.14 and therefore will not have a buoyant force and will not lift off the ground with any load. The density is lower by the factor (273 + 10)/(273+50) = 0.88 and therefore will have a buoyant force of 0.88 times the weight of the air it replaced, or about 32,000 N. The density is lower by the factor (273 + 10)/(273+50) = 0.88 and therefore will have a buoyant force of 0.12 times the weight of the air it replaced, or about 4300 N. The density is the same but the pressure of the hot air is higher by (273 + 50)/(273+10) =…The volume of a gas at 20°C is 100cm3 at normal pressure. If it is heated to 100°C, its volume becomes 125cm3 at the same pressure, then volume coefficients of the gas (at normal pressure) is? a) 0.0033/°C b) 0.0025/°C c) 0.0030/°C d) 0.0021/°C
- €2 When an air bubble rises from the bottom to the top of a freshwater lake, its volume increases by 75%. If the temperature at the bottom of the lake was 3°C and at the top was 13.5°C, how deep is the lake? Hint The lake is Question Help: Message instructor Submit Question #3 3 E 80 F3 $ 4 F4 R cr dº % m deep. 5 F5 T A 6 MacBook Air F6 & 7 F7 Y U *00 8 DII F8 - ( 9 DD F9 1 0 033. A bicycle tire has a pressure of 7.00 × 10° N/m² at a temperature of 18.0°C and contains 2.00 L of gas. What will its pressure be if you let out an amount of air that has a volume of 100 cm³ at atmospheric pressure? Assume tire temperature and volume remain constant.A 4.5-cm-diameter, 0.50-mm-thick spherical plastic shell holds carbon dioxide at 2.0 atm pressure and 25°C. CO2 molecules diffuse out of the shell into the surrounding air, where the carbon dioxide concentration is essentially zero. The diffusion coefficient of carbon dioxide in the plastic is 2.5 × 10-¹² m²/s.
- A Goodyear blimp typically contains 5300 m of helium (He) at an absolute pressure of 1.10 x 10 Pa. The temperature of the helium is 275 K. What is the mass (in kg) of the helium in the blimp? Number Units the tolerance is +/-2%An air bubble has a volume of 1.70 cm3 when it is released by a submarine 115 m below the surface of a lake. What is the volume of the bubble when it reaches the surface? Assume the temperature and the number of air molecules in the bubble remain constant during its ascent. ?cm3A hot air balloon uses the principle of buoyancy to create lift. By making the air inside the balloon less dense then the surrounding air, the balloon is able to lift objects many times its own weight. A large hot air balloon has a maximum balloon volume of 2090 m3. a. If the air temperature in the balloon is 54 °C, how much additional mass, in kilograms, can the balloon lift? Assume the molar mass of air is 28.97 g/mol, the air density is 1.20 kg/m3, and the air pressure is 1 atm.