A counter-flow double-pipe heat exchanger is to heat water from 20°C to 80°C at a rate of 1.2 kg/s. The heating is to be accomplished by geothermal water available at 160°C at a mass flow rate of 2 kg/s. The inner tube is thin-walled and has a diameter of 1.5 cm. If the overall heat transfer coefficient of the heat exchanger is 640 W/m2?K, determine the length of the heat exchanger required to achieve the desired heating.

A solid cylindrical bar conducts heat at a rate of 25 W from a hot to a cold reservoir under steady state conditions. If both the length and the diameter of this bar are doubled, the rate at which it will conduct heat between these reservoirs will be O 12.5 W. O 200 W. O 100 W. O 25 W. O 50 W.

A small metal cube with a thermal mass mc and an initial temperature 0 is dropped into a container of water that is actively maintained at a constant temperature 0w. The cube quickly comes to rest on the bottom surface of the container. The bottom surface is maintained at a constant temperature 0 (note that this is different from 0w). The thermal resistance between the cube and the water is Rcw while the thermal resistance between the bottom surface of the container and the cube is RCB. The temperature of the cube is denoted by 0c. a) Draw the system schematic indicating the assumed directions of the heat transfer rates. Label all the nodes and system parameters. b) Derive the governing equation for the temperature of the cube, 0c. c) Where does to appear in the system schematic and how does it affect the governing equations? d) Calculate the steady-state temperature of the cube, css, assuming the following system parameters: 0o = 21°C, 0B = 6°C, 0w = 0°C, Rcw = 2°C/W, and RCB = 4°C/W

A gas is contained in a chamber. Suppose that the region outside the chamber is evacuatedand the total mass of the block and the movable piston is 160 kg. When 2080 J of heat flows into the gas, the internalenergy of the gas increases by 1710 J. What is the distance (s) through which the piston rises?

A cylinder container is divided into two equal sections by thermally isolated, frictionless piston,as shown in the figure. One section contains water and the other air. The cylinder is isolated except the one face of the water section. Each section has an initial volume of 100 liter. The initial temperature of the air is 40 degees C and the water is 90 degrees C with steam quality of 10%. The water are heated slowly until the entire section of the water is filled with saturated steam. Find the final pressure and the amount of heat transported to the container. Assume: the heat transfer is a reversible process. Assume for ideal gas the following relation between p and v: (p2/p1)^((k-1)/k) = (v1/v2)^k-1 ; k=1.4

Liquid helium has a very low boiling point, 4.2 K, as well as a very low latent heat of vaporization, 2.00  104 J/kg. If energy is transferred to a container of liquid helium at the boiling point from an immersed electric heater at a rate of 19.0 W, how long does it take to boil away 2.30 kg of the liquid? _________________min

assume adibatic. other solutions are wrong