Concept explainers
Quenching is the process of immersing a hot metal object in a bath for a specified time to improve properties such as hardness. A copper sphere 25 mm in diameter, initially at 300°C, is immersed in a bath at 0°C. Measurements of the sphere’s temperature versus time are shown here. Plot the data and find a functional description of the data.
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System Dynamics
- 3. A metallic rod 20 cm long is heated to a uniform temperature of 100° C. At t = 0 the ends of the bar are plunged into an ice bath at 0° C and thereafter maintained at this temperature. Find an expression for the temperature u(x, t) if the bar is made of cast iron. Material a (cm²/s) Silver 1.71 Copper 1.14 Aluminum 0.86 Cast iron 0.12 Granite 0.011 Brick 0.0038 Water 0.00144 Table 1: Thermal Diffusivity Constants for Common Materialsarrow_forwardWhat will be the rise in temperature in 30 minutes of a block of copper of 500-gram mass if it is joined to a cylindrical copper rod 20 cm long and 3.0 mm in diameter when a temperature difference of 80 degree Celsius is maintained between ends of the rod? The thermal conductivity of copper is 1.02 cal/cm2-sec-°C/cm (neglect heat losses). Please include FBDarrow_forwardThe Philippine ten-peso coin (P10) is the second largest denomination coin of the Philippine peso. The current version, issued since 2018, has a diameter of d, = 27.0000 mm and a thickness of họ = 2.0500 mm. When the coin is subjected to a temperature change of 100 C°, the diameter of the coin increases by 0.11 percent. Suppose the coefficient of linear expansion of the coin is unknown, which of the following expressions should you use to compute for it? *arrow_forward
- The following graph shows the thermal behavior of 2 kg of a material called Uniandesato undergoing a solid-liquid phase transition. In a container, thermally insulated from the outside, 20 kg of liquid water at a temperature of 80°C are placed. In addition to this, an unknown amount of Uniandesato in a 100% solid state at its melting temperature (10°C) is added. The specific heat of water is 4186 J/kg°C. a) If the system reaches an equilibrium temperature of 60°C, calculate the initial amount of Uniandesato added to the container. b) Calculate the change in entropy during this process and show that it is consistent with the Second Law of Thermodynamics. Hint: Extract the necessary information to solve this problem from the graph.arrow_forwardThe below shown graph is drawn from the tabulated values of steel which we measured during the experiment of thermal conductivity: (Consider the value of heater power (Q') and the area of cross section (A) of the material from the tabulated values) x-axis 1 unit = 1 cm y-axis 1 unit = 10°C 80- 70- 60- 50- 40- 30- 20- 10- Distance X in cm 3 4 6. 8. 10 Calculate the following: Thermal conductivity of steel Value Calculated quantities Temperature T degree Celsiusarrow_forward8) Consider two liquids, A and B. with temperatures Te > TA. The two objects are put into thermal contact for a time period. Without just saying 'heat flows from hot to cold' how would you prove to someone that a quantity of heat flowed from B to Á. (think of James Joule's experiments) 9) If the temperature of the sun were to suddenly double, by what multiplicative factor would the thermal radiation change ? Show Workarrow_forward
- A J- type thermocouple is used to measure the temperature in a heating process. Sheath material used is SS316. The length of the sheath is 13mm and thickness is 0.3mm. Find the time constant of the sheath. Material Q(kg/m3)s(J/Kg - °c)K(W/m-k) Platinum 21450 130 71.6 SS304 8030 500 21.4 SS316 7990 500 21.4 SS410 7750 460 24.9 Air 1.20 1005 0.025 MgO Powder 3580 877 26.8 Silicon compound3210 800 3 Time constant of the bare material is, T=arrow_forward1.)An aluminum tank with a volume of 1000 liters is filled with gasoline. Both are at a temperature of 12°C. The tank is transported to a place where the temperature is 37° and, due to the difference between the volumetric expansion coefficients of the metal and the liquid, the ebb of the tank. Assuming the tank expands like a massive volume of aluminum, how many liters of gasoline overflow from the tank? Data: βaluminum=7*10-5/ºC and βgas=9.5*10-4/ºCarrow_forwardA J- type thermocouple is used to measure the temperature in a heating process. Sheath material used is SS316. The length of the sheath is 10mm and thickness is 0.2mm. Find the time constant of the sheath. Material Q(kg/m3) s(J/Kg - oc) K(W/m-k) Platinum 21450 130 71.6 SS304 8030 500 21.4 SS316 7990 500 21.4 SS410 7750 460 24.9 Air 1.20 1005 0.025 MgO Powder 3580 877 26.8 Silicon compound 3210 800 3 Time constant of the bare material is, T= Answerarrow_forward
- A team of students tests a material for its thermal conductivity (k). After 20 minutes in a heat box, the temperature is 48° C inside the box and 28° C on top of the material. The following data is true about this test: Area of material = .0225 m2 Thickness of material = .0127 m Light bulb = 25 W What is the thermal conductivity constant for the material? Calculate the amount of energy transferred through the material. Determine the R-value of the material. Based on your calculations, would the material be a reasonable choice for home insulation? Yes of Noarrow_forwardA one-meter long bar has been heated unevenly, with temperature in °C at a distance z meters from one end at time t given by H(2, t) = 110e 0.06t sin(rz) 0 < <1. (a) On a sheet of paper, sketch a graph of H against z for t = 0 and t = 1. Use this graph to select all correct statements below. A. When t = 0, the rod is the same temperature throughout B. The rod is coldest at the r = 0 end, and warmest at the a = 1 and C. The two ends of the rod remain at 0°C D. The rod is coldest in the middle E. The middle of the rod gets colder over time F. The closer you are to the middle of the rod, the greater the temperature change from t = 0 to t = 1 G. None of the above %3D (b) On a sheet of paper, sketch a graph of H against t for a= 1/8, a= 1/4, and a = 1/2. Use this graph, and your observations from the previous graph, to select all correct statements below. JA. As time goes on, all part of the rod approach the same temperature B. The temperature near the middle of the rod changes most quicky…arrow_forward= Consider a large plane wall of thickness L=0.3 m, thermal conductivity k = 2.5 W/m.K, and surface area A = 12 m². The left side of the wall at x=0 is subjected to a net heat flux of ɖo = 700 W/m² while the temperature at that surface is measured to be T₁ = 80°C. Assuming constant thermal conductivity and no heat generation in the wall, (a) express the differential equation and the boundary equations for steady one- dimensional heat conduction through the wall, (b) obtain a relation for the variation of the temperature in the wall by solving the differential equation, and (c) evaluate the temperature of the right surface of the wall at x=L. Ti до L Xarrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning