At 27°C and 1 ATP, a volume of air abruptly shrank by half. Temperature and pressure must be determined.
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At 27°C and 1 ATP, a volume of air abruptly shrank by half. Temperature and pressure must be determined.
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- An automobile tire is inflated with air originally at 10.0°C and normal atmospheric pressure. During the process, the air is compressed to 31.0% of its original volume and the temperature is increased to 48.0°C. (a) What is the tire pressure in pascals?(b) After the car is driven at high speed, the tire's air temperature rises to 85.0°C and the tire's interior volume increases by 3.00%. What is the new tire pressure (absolute) in pascals?Problem 8: Hot air balloons float because the air inside an inflatable compartment is heated. Consider such a balloon that has an inflatable compartment of maximum volume 1960 m3 and a basket with passengers of total mass 280 kg. Part (a) To what temperature, in Celsius degrees, would the air inside the balloon have to be heated in order for the balloon to lift off the ground? Assume the molar mass of air is 28.97 g/mol and its density is 1.20 kg/m3. Part (b) When the balloon reaches the highest point of its flight (around 2000 m), the air pressure has dropped to 80% of the pressure at ground level, and the density has dropped to 85% of the previous value. What temperature, in degrees Celsius, must the air in the balloon be to keep it floating at this altitude?A weather balloon rises through the atmosphere, its volume expanding from 4.9 m3 to 14 m3 as the temperature drops from 21 ∘C to -10 ∘C. If the initial gas pressure inside the balloon is 1.0 atmatm, what is the final pressure?
- People that live at high altitudes often notice that sealed bags of food are puffed up because the air inside has expanded since they were sealed at a lower altitude. In one example, a bag of potato chips was packed at a pressure of 1.00atm and a temperature of 20.5 degrees celcius. The bag was then transported to Santa Fe. The sealed bag of potato chips then finds its way to a summer picnic where the temperature is 31.6 degrees celcius, and the volume of air in the bag has increased to 1.4 times its original value. At the picnic in Santa Fe, what is the pressue, in atmospheres, of the air in the bag?An automobile tire is inflated with air originally at 10.0°C and normal atmospheric pressure. During the process, the air is compressed to 27.0% of its original volume and the temperature is increased to 39.0°C. (a) What is the tire pressure in pascals? Pa (b) After the car is driven at high speed, the tire's air temperature rises to 85.0°C and the tire's interior volume increases by 3.00%. What is the new tire pressure (absolute) in pascals? PaStep 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.
- 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 certain amount of gas at 25.0°C and at a pressure of 0.650 atm is contained in a glass vessel. Suppose that the vessel can withstand a pressure of 2.00 atm. How high can you raise the temperature of the gas without bursting the vessel? In other words, at what temperature will the glass vessel shatter, in degrees Celsius.During an all-night cram session, a student heats up a 0.807 liter (0.807 x 10- 3 m3) glass (Pyrex) beaker of cold coffee. Initially, the temperature is 15.5 °C, and the beaker is filled to the brim. A short time later when the student returns, the temperature has risen to 98.0 °C. The coefficient of volume expansion of coffee is the same as that of water. How much coffee (in cubic meters) has spilled out of the beaker?