Written Question: You have just started your new job at Gas-n-Giggles, a company that specializes in fossil-fuel based baby toys. Your first task is to analyze three design proposals for a gasoline-powered machine to entertain babies. Each design has air (use C₁ = 5/2R) in a cylinder with a piston that moves down or up in response to cooling/heating. The added heat in the various processes comes from burning gasoline (35MJ/L). The processes associated with the three designs (for a fixed baby weight) may be modeled by the following PV diagrams, where in all cases, the temperature for the bottom-left corner of the cycle is 300K. P(kPa) 200 120 P (KPM) -isothermal P(kPa) ✓adiabatic 120 120 (B) →V IOL 30L IOL 30L V 10 L 30L Pediatric psychologists have found that the happiness of a baby on such a device is proportional to the net work performed on them per time, regardless of the design. Which if the three designs is most efficient if we wish to produce a certain amount of net work by burning the least amount of fuel? For this design, what amount of gasoline do we need to burn per hour if we want the baby to move up and down 10 times per minute?

Unreasonable results. (a) Find the temperature of 0.360 kg of water, modeled as an ideal gas, at a pressure of 1.01105 Pa if it has a volume of 0.615 m3. (b) What is unreasonable about this answer? How could you get a better answer?

One process for decaffeinating coffee uses carbon dioxide ( M=44.0 g/mol) at a molar density of about 14,0 mol/m3 and a temperature of about 60 . (a) Is CO2 a solid, liquid, gas, or supercritical fluid under those conditions? (b) The van der Waals constants for carbon dioxide are a=0.3658 Pa m6/mol2 and b=4.286105 m3/mol. Using the van der Waals equation, estimate pressure of CO2 at that temperature and density. `

Calculate the length of a 1-meter rod of a material with thermal expansion coefficient a when the temperature is raised from 300 K to 600 K. Taking your answer as the new initial length, find the length after the rod is cooled back down to 300 K. Is your answer 1 meter? Should it be? How can you account for the result you got?

Five bicyclists are riding at the following speeds: 5.4 m/s, 5.7 m/s, 5.8 m/s, 6.0 m/s, and 6.5 m/s. (a) What is their average speed? (b) What is their rms speed?

A tank contains 111.0 g chlorine gas l2), which is at temperature 82.0 and absolute pressure 5.70105 Pa. The temperature of the air outside the tank is 20.0 . The molar mass of Cl2 is 70.9 g/mol. (a) What is the volume of the tank? (b) What is the internal energy of the gas? (c) What is the work done by the gas if the temperature and pressure inside the tank drop to 31.0 and 3.80105 Pa, respectively, due to a leak?

One mole of an ideal gas is initially in a chamber of volume 1.0102 m3 and at a temperature of 27 . (a) How much heat is absorbed by the gas when it slowly expands isothermally to twice its initial volume? (b) Suppose the gas is slowly transformed to the same final state by first decreasing the pressure at constant volume and then expanding it isobarically. What is the heat transferred for this case? (c) Calculate the heat transferred when the gas is transformed quasi-statically to the same final state by expanding it isobarically, then decreasing its pressure at constant volume.

(a) Calculate the work done by the gas along the closed path shown below. The curved section between R and S is semicircular. (b) If the process is carried out in the opposite direction, what is the work done by the gas?

What is the average kinetic energy in joules of hydrogen atoms on the 5500 surface of the Sun? (b) What is the average kinetic energy of helium atoms in a legion of the solar corona where the temperature is 6.00105 K ?

One mole of an ideal gas doubles its volume in a reversible isothermal expansion. (a) What is the change in entropy of the gas? (b) If 1500 J of heat are added in this process, what is the temperature of the gas?