Heat Engines & PV Diagrams Practice Problems
A gasoline-powered engine follows the pV trajectory shown in the figure below. Calculate the i) useful work (Wout), ii) heat extracted from the hot reservoir (QH), and iii) thermal efficiency (η).
A prototype thermal engine operates on a closed cycle that includes one isobaric, one isochoric, and one isothermal process, as illustrated in the figure below. The working substance inside the engine is 1.00 mol of air, which has a molar heat capacity ratio of 1.40. The cycle starts with an initial temperature (TA) of 290 K. The engine runs at a rate of 5 cycles per second. Determine the output power of the thermal engine.
A heat engine undergoes a cyclic process consisting of three steps: AB, BC, and CA. The engine utilizes 1 mol of helium as its working fluid. Calculate the net change in internal energy, the net work done by the engine, and the net heat exchanged by the engine during one cycle.
In a laboratory experiment, 0.300 moles of helium is used as the working fluid in a thermal engine. The helium undergoes an isothermal expansion from an initial volume of 2.50 × 10-3 m3 to 7.50 × 10-3m3 at a temperature of 400 K, followed by an isochoric cooling to 320 K, an isothermal compression to a volume of 2.50 × 10-3 m3, and finally, isochoric heating to a temperature of 400 K. Calculate i) the work done in one cycle and ii) the thermal efficiency of the engine.
The dynamo on a bicycle generates electricity as we pedal. The dynamo has a per-cycle work output of 50 J and waste heat output of 80 J. Determine the dynamo's thermal efficiency during your bike ride.
In an underwater research facility, scientists built a power generator to provide sustainable energy for their deep-sea operations. This novel generator uses a specific fuel with an energy density of 40 MJ/kg to produce 95 MW of power. With an efficiency of 35%, what is the fuel consumption rate of this underwater power generator in kg/s?
A motorbike has an engine with an output power of 15 horsepower and a rotational speed of 3600 rpm. Assume that the engine operates in a closed cycle and has a thermal efficiency of 25%. Calculate the engine's i) work and ii) heat output in one cycle.
A mechanical engineer designed a thermal engine that operates using the cycle shown in the figure below. Determine i) the heat extracted (QH) from the heat source ii) and the thermal efficiency (η)
A 1200 W portable power plant runs on liquid petroleum. The power plant consumes 0.50 L of liquid petroleum per hour. The energy density per volume unit of the used liquid petroleum is 35 MJ/L. Calculate the thermal efficiency of this power plant.
A mechanical engineering student built a coal-fired power plant prototype. First, the coal is burned in a boiler, producing 2750 W of heat. The heat from the burning coal is used to boil water, and the produced high-pressure steam causes the blades of a turbine to spin. As a result, 220 W of electrical power is generated. Determine the prototype power plant's efficiency.