1. In an industrial fabrication process, a fluid, with density p = 800 kg/m³ and specific heat capacity c = 5000 J/kg.Co, emerges from a tank at a temperature, T₁ = 400 °C. The fluid then enters a metal pipe with inner radius a = 2.0 cm and outer radius b = 3.0 cm and thermal conductivity k = 180 W/m.Co. Outside the pipe the temperature is fixed at Tout = 15 °C. If the fluid flows at speed v = 8.0 m/s and the length of the pipe is L = 25 m, what is the temperature of the fluid at the end of the pipe? (Answer: 83 °C)

(a) At what temperature does water boil at an altitude of 1500 m (about 5000 ft) on a day when atmospheric pressure is 8.59104N/m2 ? (b) What about at an altitude of 3000 m (about 10,000 ft) when atmospheric pressure is 7.00104N/m2 ?

A spherical shell has inner radius 3.00 cm and outer radius 7.00 cm. It is made of material with thermal conductivity k = 0.800 W/m C. The interior is maintained at temperature 5C and the exterior at 40C. After an interval of time, the shell reaches a steady state with the temperature at each point within it remaining constant in time. (a) Explain why the rate of energy transfer P must be the same through each spherical surface, of radius r, within the shell and must satisfy dTdr=P4kr2 (b) Next, prove that 5dT=P4k0.030.07r2dr where T is in degrees Celsius and r is in meters. (c) Find the rate of energy transfer through the shell. (d) Prove that 5TdT=1.840.03rr2dr where T is in degrees Celsius and r is in meters. (e) Find the temperature within the shell as a function of radius. (f) Find the temperature at r = 5.00 cm, halfway through the shell.

(a) What is me gauge pressure in a 25.0C car tire containing 3.60 mol of gas in a 30.0 L volume? (b) What will its gauge pressure be if you add 1.00 L of gas originally at atmospheric pressure and 25.0C ? Assume the temperature returns to 25.0C and me volume remains constant.