First Law of Thermodynamics: Energy Conservation And solve the problems for engineer and engineering students.

Energy 

A basic idea is that energy can be stored within systems in various forms. Energy also can be converted from one form to another and transferred between systems. For closed systems, energy can be transferred by work and heat transfer

Example 1: a. To illustrate the proper use of units in the calculation of such terms, consider a system having a mass of 1 kg whose velocity increases from 15 m/s to 30 m/s while its elevation decreases by 10 m at a location where g = 9.7 m/s2.  b. For a system having a mass of 1 lb whose velocity increases from 50 ft/s to 100 ft/s while its elevation decreases by 40 ft at a location where g = 32.0 ft/s2.
Both a and b, what are the value of ΔKE and ΔPE?

Example 2: Let us evaluate the power required for a bicyclist traveling at 5.6 m/s to overcome the drag force imposed by the surrounding air. This aerodynamic drag force is given by                                  , where CD is a constant called the drag  coefficient, A is the frontal area of the bicycle and rider, and ρ is the air density. Calculate the power that required for a bicyclist if using typical values: CD = 0.88, A = 1.2 m2, and ρ = 0.0005 kg/m3 together with V = 5.6 m/s.

Example 1: a. To illustrate the proper use of units in the calculation of such terms, consider a system having a mass of 1 kg whose velocity increases from 15 m/s to 30 m/s while its elevation decreases by 10 m at a location where g = 9.7 m/s2.  b. For a system having a mass of 1 lb whose velocity increases from 50 ft/s to 100 ft/s while its elevation decreases by 40 ft at a location where g = 32.0 ft/s2.
Both a and b, what are the value of ΔKE and ΔPE? 

Example 5: Four kilograms of a certain gas is contained within a piston– cylinder assembly. The gas undergoes a process for which the pressure–volume relationship is  pV*1.5= constant. The initial pressure is 3 bar, the initial volume is 0.1 m3, and the final volume is 0.2 m3. The change in specific internal energy of the gas in the process is u2 - u1 = - 4.6 kJ/kg. There are no significant changes in kinetic or potential energy. Determine the net heat transfer for the process, in kJ

Example 6: Air is contained in a vertical piston–cylinder assembly fitted with an electrical resistor. The atmosphere exerts a pressure of 14.7 lbf/in.2 on the top of the piston, which has a mass of 100 lb and a face area of 1 ft2. Electric current passes through the resistor, and the volume of the air slowly increases by 1.6 ft3 while its pressure remains constant. The mass of the air is 0.6 lb, and its specific internal energy increases by 18 Btu/lb. The air and piston are at rest initially and finally. The piston–cylinder material is a ceramic composite and thus a good insulator. Friction between the piston and cylinder wall can be ignored, and the local acceleration of gravity is g = 32.0 ft/s2.


Example 6 (continue…) Determine the heat transfer from the resistor to the air, in Btu, for a system consisting of (a) the air alone, (b) the air and the piston.


Example 7: During steady-state operation, a gearbox receives 60 kW through the input shaft and delivers power through the output shaft. For the gearbox as the system, the rate of energy transfer by heat is   Q(rate)=-hA(Tb-Tf)   , where h is a constant, is the outer surface area of the gearbox, Tb = 300 K (27°C) is the temperature at the outer surface, and Tf = 293 K (20°C) is the temperature of the surrounding air away from the immediate vicinity of the gearbox. For the gearbox, evaluate the heat transfer rate and the power delivered through the output shaft, each in kW. 

Example 8: A silicon chip measuring 5 mm on a side and 1 mm in thickness is embedded in a ceramic substrate. At steady state, the chip has an electrical power input of 0.225 W. The top surface of the chip is exposed to a coolant whose temperature is 20°C. The rate of energy transfer by heat between the chip and the coolant is given by    Q(rate)=-hA(Tb-Tf)   , where Tb and Tf are the surface and coolant temperatures, respectively, A is the surface area, and  If heat transfer between the chip and the substrate is negligible, determine the surface temperature of the chip, in °C.