1. A copper rod is 0.50 m long and has a cross-sectional area of 4.0×10-*m². One end of the rod is kept at 30 °C, while the other end is at 75 °C. The sides of the rod are insulated so that heat losses through the sides are negligible. (a) Find how much heat flows through the rod per second. (b) What is the temperature at 0.30 m from the higher-temperature end of the od? The thermal conductivity of copper is 390//s m °C:

Το TL K₁, A, L₁ x=0 Та K2, A, L₂ Tb K₁, A, L₁ L "Create a thermal resistance diagram from a to L and formulate an equation to calculate K2 in terms of the other variables."

An aluminum pipe has a length of 75 m at a temperature of 18°C. An adjacent steel pipe at the same temperature is 5 mm longer than the aluminum pipe. At what temperature (°C) will the aluminum pipe be 15 mm longer than the steel pipe? (Assume that the coefficients of thermal expansion of aluminum and steel are αa = 23 x 10^–6/°C and αs = 12 x 10^–6/°C, respectively.)

Exercise 2.3:Assume that the thermal conductivity of copper is four times that of brass. Two metalrods made of copper and brass are each 20 cm long and 2.0 cm in diameter. The rods are placed end to end. The free end of the copper rod is maintained at 1000C and the free end of the brass rod is maintained at 00C. (i) What is the equilibrium temperature at the copper-brass junction? |(ii)If the thermal conductivity of copper is 390 J/m0C, at what rate, in watts, does heat flow through the rods

In the diagram below, metal 1 is made of gold and metal 2 is aluminum. Both bars have the same length and area of cross-section but their thermal conductivities are different. The temperature Th is maintained at a constant 88.0°C at the end A while the temperature T, at the end B is maintained at 19.0°C. A. T metal 1 metal 2 T (a) What is the temperature T; at the junction of the two bars? The thermal conductivity of gold is 318 J/(s · m · °C) and that for aluminum is 220 J/(s• m · °C). °C (b) If metals 1 and 2 are now interchanged, but the values of Th and T, are the same as in part (a), what will be the temperature of the junction? °C

The figure shows the cross section of a wall made of three layers. The thicknesses of the layers are L₁, L2=0.750 L₁, and L3 = 0.350 L₁. The thermal conductivities are k₁, k₂ = 0.840 k₁, and k3 = 0.780 k₁. The temperatures at the left and right sides of the wall are TH = 23 °C and Tc = -10 °C, respectively. Thermal conduction is steady. (a) What is the temperature difference AT2 across layer 2 (between the left and right sides of the layer)? If k2 were, instead, equal to 1.160 k₁, (b) would the rate at which energy is conducted through the wall be greater than, less than, or the same as previously, and (c) what would be the value of AT2? TH k₁ L₁ kg|kz kq L₂ L3 Tc

3.4 Estimate the rate of heat loss due to radiation from a covered pot of water at 95 ° C. How does this compare with the 60 W that is lost due only to convection and conduction losses? What amount of energy input would be needed to maintain the water at its boiling point for 30 minutes? The polished stainless steel pot is cylindrical, 20 cm in diameter and 14 cm high, with a tight-fitting flat cover. The air temperature in the kitchen is about 25 ° C. State any assumptions you make in deriving your estimates

A boiler furnace wall must have a heat loss no greater than 700 Btu/hr~ft2 and is madeof a material with a thermal conductivity of 0.60 Btu/hr~ft~F. The inner wall surfacetemperature is '2000°F, and the outer surface temperature is 800°F. What wall thick~ness is required?

At a temperature of 21.4°C the hole in a steel plate has an area of 8.80 x 10- m2. You heat the plate until the area of the hole increases to 8.97 x 10- m2, which allows a steel rod to just slip through this hole. What is the final temperature of the plate? The coefficient of linear expansion of steel is 12 × 10-0/°C.

A plane wall is constructed of a material having a thermal conductivity that varies as the square of the temperature according to the relation k =k0(1+βT^2 ). Derive an expression for the heat transfer in such a wall. Find the heat transfer per unit area through the composite wall Assume one-dimensional heat flow.