How to solve these two questions of Thermal Physics?

1.

cm A hot bath at Th = 193.1 \"C is connected to a cold bath at Tc = 14.3 \"C by an insulated rod as shown in the diagram below (Figure 1). The rod is made from two cylindrical components: wood of length Lw that is connected to the hot bath, and rubber of length L, that is connected to the cold bath. Thejunction between the wood and rubber has a temperature Tj. The cross-sectional area of the wood and rubber components are the same. Wood has a thermal conductivity value kw = 0.080W/m ' K and rubber has kr = 0.20W/m ' K. Thermal insulation Junction temperature 7}- (Diagram is not to scale) Figure 1: Schematic of the described hot and cold baths at temperatures Th and Tc, respectively, connected via an insulated cylindrical rod consisting of wood of length Lw next to the hot bath, and rubber of length L, next to the cold bath. The temperature of thejunction between the wood and rubber is T} Part 1) If Lw = Lr, what is the steady-state temperature at the junction between the wood and rubber, T} ? T}- = 65.4 C Your last answer was interpreted as follows: 65.4 Part 2) If the cross-sectional area of the rod is 38.7 cm2 and the rate of energy ow through the rod is 199.8 W, what is the length of each individual component? Part 3) If the cross-sectional area remains the same but the length of the rubber component is now double that of the wood component, what is the temperature at the junction? Question: Figure 1 shows an Otto cycle, this is the idealised cycle used in common gasoline engines. During the cycle, a fuel/air mixture is drawn into a cylinder, it is compressed, a spark ignites the gas, the gas expands, the outlet valve is then opened and the gas/fuel mixture exhausted from the cylinder. In this cycle, the compression and expansion of the gas are adiabatic. Otto cycle (Not to scale) Figure 1: A PV plot depicting the Otto cycle. The gas goes right along horizontal pathway labelled 1 and then goes up and left along an adiabatic pathway labelled 2. Following that, the gas goes up along a vertical pathway labelled 3 and then goes down and right along an adiabatic pathway labelled 4. The gas then goes down along a vertical pathway labelled 5, returning to the position that pathway 1 took it, before going left along a horizontal pathway labelled 6, to the condition in which the gas started. The x-axis represents volume and the y-axis represents pressure. Part 1) During which process on the diagram is mechanical energy extracted from the system? Your last answer was interpreted as follows: 4 Part 2) The fuel/air mix is drawn into a 206 mL cylinder during process 1 at a temperature of 21.9 "C and a pressure of 1.03 atm. How many mols of fuel/air mixture are drawn into the cylinder? This process is labelled 1 in Figure 1. Part 3) The compression shown as 2 in Figure 1 happens very quickly and so is adiabatic. At the end of the compression (stroke), the volume of the gas is 26.5 mL. Assume the air/fuel is is diatomic. What is the pressure of the gas at the end of 2? Part 4) What is the temperature of the gas at the end of this compression? T=_C Part5) How much work is done on the gas during the compression? W=J Part 6) During the expansion, the gas does 367 J of work. Calculate the power output of a four-cylinder engine running at 2719 rpm. A four-cylinder engine consists of four cylinders, all doing work. Rpm stand for revolutions per minute, only half these revolutions produce work, the others are intake and outtake strokes which require negligible work. What power does this engine produce? P=w