bubble remains equal to the water temperature. The pressure in the tank is very high, so the initial volume of the air is ne
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A submerged scuba diver, 11 m below the surface of the water, blows a bubble of air from the valve of her tank. The final volume of the bubble is 3.7 cm3, and the temperature of the air is that of the water, 15°C. Assume that the temperature of the air in the bubble remains equal to the water temperature. The pressure in the tank is very high, so the initial volume of the air is negligible compared with the final volume at the bubble.
Calculate how much heat the bubble absorbs as it forms. Calculate how much work the bubble does on the surrounding water.
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Solved in 3 steps
- 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.The absolute pressure in your car tires is 3.7 × 105 Pa at a temperature of 35.0°C when you drive it onto a ferry boat to Alaska a. What is the absolute pressure of the tires, in pascals, later when the temperature has dropped to -40.0°C? Assume the volume of each tire does not change.
- The rms speed of an oxygen molecule (O2) in a container of oxygen gas is 614 m/s. What is the temperature of the gas?One mole of hydrogen gas (molar mass = 2.0 g/mol) has an rms velocity of 2.0 x 10° m/s. To what temperature on the Celsius scale does this correspond? 3.2 x 105 °C O 4.8 x 104 C 3.2 x 102 °C 48°C 6.9°CA bubble having a diameter of 62 cm is re- leased from a depth of 4.6 m from the bottom of a swimming pool. The temperature of the water at the surface is 21°C, whereas it is 15°C at the point of release. What will the diameter of the bubble be when it reaches the surface? The acceleration of gravity is 9.8 m/s² and the density of water is 1000 kg/m³. Answer in units of cm.
- A bicycle tire has a pressure of 6.80 ✕ 105 N/m2 at a temperature of 19.0°C and contains 2.30 L of gas. What will its pressure be (in Pa) if you let out an amount of air that has a volume of 120 cm3 at atmospheric pressure? Assume tire temperature and volume remain constant. _________PaAn 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 38.0°C. (a) What is the tire pressure in pascals? Use the ideal gas law to find the pressure inside the tire from its volume and temperature. 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?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%
- Two ideal gases have the same mass density and the same absolute pressure. One of the gases is helium (He), and its temperature is 131 K. The other gas is neon (Ne). What is the temperature of the neon?Two massless, frictionless pistons are inside a horizontal tube opened at both ends. A 10-cm-long thread connects the pistons. The cross-sectional area of the tube is 20 cm2. The pressure and temperature of gas between the pistons and the outside air are the same and are equal to P = 1.0×10^5 N/m^2 and T = 21C. At what temperature will the thread break if it breaks when the tension reaches 32 N ?500 J of work are done to compress the gas while, in the same process, 1800 J of heat energy are transferred from the gas to the environment. Afterward, what is the rms speed of the molecules? Express your answer with the appropriate units.