* 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_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_forwardA 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_forward
- An 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(a) If you shake a jar full of jelly beans of different sizes, the larger beans tend to appear near the top and the smaller ones tend to fall to the bottom. Why? (b) Does this process violate the second law of thermodynamics?arrow_forward
- Suppose an ideal (Carnot) heat pump could be constructed for use as an air conditioner. (a) Obtain an expression for the coefficient of performance (COP) for such an air conditioner in terms of Tb and Tc. (b) Would such an air conditioner operate on a smaller energy input if the difference in the operating temperatures were greater or smaller? (c) Compute the COP for such an air conditioner if the indoor temperature is 20.0C and the outdoor temperature is 40.0C.arrow_forwardIf a gas is compressed isothermally, which of the following statements is true? (a) Energy is transferred into the gas by heat. (b) No work is done on the gas. (c) The temperature of the gas increases. (d) The internal energy of the gas remains constant. (e) None of those statements is true.arrow_forward(a) Prepare a table like Table 18.1 for the following occurrence. You toss four coins into the air simultaneously and then record the results of your tosses in terms of the numbers of heads (H) and tails (T) that result. For example, HHTH and HTHH are two possible ways in which three heads and one tail can be achieved. (b) On the basis of your table, what is the most probable result recorded for a toss? In terms of entropy, (c) what is the most ordered macrostate, and (d) what is the most disordered?arrow_forward
- (a) What is the best coefficient of performance for a heat pump that has a hot reservoir temperature of 50.0C and a cold reservoir temperature of 20.0C ? (b) How much heat transfer occurs into the warm environment if 3.60107J of work (10.0kWh) is put into it? (c) If the cost of this work input is 10.0cent/kWh, haw does its cost compare with the direct heat transfer achieved by burning natural gas at a cost of 85.0 cents per therm. (A therm is a common unit of energy for natural gas and equals 1.055108J .)arrow_forwardA biology laboratory is maintained at a constant temperature of 7.00C by an air conditioner, which is vented to the air outside. On a typical hot summer day, the outside temperature is 27.0C and the air-conditioning unit emits energy to the outside at a rate of 10.0 kW. Model the unit as having a coefficient of performance (COP) equal to 40.0% of the COP of an ideal Carnot device. (a) At what rate does the air conditioner remove energy from the laboratory? (b) Calculate the power required for the work input. (c) Find the change in entropy of the Universe produced by the air conditioner in 1.00 h. (d) What If? The outside temperature increases to 32.0C. Find the fractional change in the COP of the air conditioner.arrow_forward(a) What is the best coefficient of performance for a refrigerator that cools an environment at 30.0C and has heat transfer to another environment at 45.0C ? (b) How much work in joules must be done for a heat transfer of 4186 kJ from the cold environment? (c) What is the cost of doing this if the work costs 10.0 cents per 3.60106J (a kilowatthour)? (d) How many kJ of heat transfer occurs into the warm environment? (e) Discuss what type of refrigerator might operate between these temperatures.arrow_forward
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