* Imagine that the helium balloon from the previous problem was placed in an evacuated container of volume
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- A power plant has been proposed that would make use of the temperature gradient in the ocean. The system is to operate between 20.0C (surface water temperature) and 5.00C (water temperature at a depth of about 1 km). (a) What is the maximum efficiency of such a system? (b) If the useful power output of the plant is 75.0 MW, how much energy is absorbed per hour? (c) In view of your answer to part (a), do you think such a system is worthwhile (considering that there is no charge for fuel)?arrow_forwardA power plant has been proposed that would make use of the temperature gradient in the ocean. The system is to operate between 20.0C (surface water temperature) and 5.00C (water temperature at a depth of about 1 km). (a) What is the maximum efficiency of such a system? (b) If the useful power output of the plant is 75.0 MW, how much energy is absorbed per hour? (c) In view of your answer to part (a), do you think such a system is worthwhile (considering that there is no charge for fuel)?arrow_forwardIn a cylinder of an automobile engine, immediately after combustion the gas is confined to a volume of 50.0 cm3 and has an initial pressure of 3.00 106 Pa. The piston moves outward to a final volume of 300 cm3, and the gas expands without energy transfer by heat, (a) What is the final pressure of the gas? (b) How much work is done by the gas in expanding?arrow_forward
- A hand—driven tire pump has a piston with a 2.50cm diameter and a maximum stroke of 30.0 cm. (a) How much work do you do in one stroke if the average gauge pressure is 2.40105N/m2 (about 35 psi)? (b) What average force do you exert on the piston, neglecting friction and gravitational force?arrow_forwardAn air bubble starts rising from the bottom of a lake. Its diameter is 3.60 mm at the bottom and 4.00 mm at the surface. The depth of the lake is 2.50 m, and the temperature at the surface is 40.0C. What is the temperature at the bottom of the lake? Consider the atmospheric pressure to be 1.01 105 Pa and the density of water to be 1.00 103 kg/m3. Model the air as an ideal gas. 53. Use the ideal gas law for the bottom (point 1) and the surface (point 2) of the lake. At the surface, the pressure is atmospheric pressure. However, at the bottom it is equal to to the sum of the atmospheric pressure and the pressure due to 2.50 m column of water. P2=1.01105PaP1=P2+WghWP1=1.01105Pa+(1.00103kg/m3)(9.81m/s2)(2.50m) Use the ideal gas law (Eq. 19.17). T1=P1V1P2V2T2 The volume ratio at the bottom and top of the lake can be calculated with the diameters given. V1V2=43r1343r23=(1.82.0)3 T1=P1P2(V1V2)T2T1=1.01105Pa+(1.00103kg/m3)(9.81m/s2)(2.50m)1.01105Pa(1.802.00)3(40.0+273.15K)T1=284Karrow_forwardAir (a diatomic ideal gas) at 27.0C and atmospheric pressure is drawn into a bicycle pump (Figure P17.53) that has a cylinder with an inner diameter of 2.50 cm and length 50.0 cm. The downstroke adiabatically compresses the air, which reaches a gauge pressure of 8.00 105 Pa before entering the tire. We wish to investigate the temperature increase of the pump. (a) What is the initial volume of the air in the pump? (b) What is the number of moles of air in the pump? (c) What is the absolute pressure of the compressed air? (d) What is the volume of the compressed air? (e) What is the temperature of the compressed air? (f) What is the increase in internal energy of the gas during the compression? What If? The pump is made of steel that is 2.00 mm thick. Assume 4.00 cm of the cylinders length is allowed to come to thermal equilibrium with the air. (g) What is the volume of steel in this 4.00-cm length? (h) What is the mass of steel in this 4.00-cm length? (i) Assume the pump is compressed once. After the adiabatic expansion, conduction results in the energy increase in part (f) being shared between the gas and the 4.00-cm length of steel. What will be the increase in temperature of the steel after one compression? Figure P17.53arrow_forward
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