During an experiment conducted in a lab at 25°C, a student measured that a Carnot refrigerator withdraws 500 J of heat from the refrigerated space maintained at -5°C. How many joules of heat are delivered to the lab?

A spacecraft's Carnot heat engine is designed to work between 100℃ and 600℃ to generate energy.  This energy powers a Carnot cooling system that regulates the spacecraft's internal temperature. The cooling system works between -10°C and 20°C. Determine, in joules, the ratio of heat energy discharged by the cooling system to the energy consumed by the heat engine.

A natural gas power plant generates 600 MW of electricity by burning natural gas at a rate of 1800 m³ per hour. The density of natural gas is  0.75 kg/m³ at standard temperature and pressure. If the natural gas is stored in a cylindrical tank with a diameter of 50. meters, how tall must the tank be to operate the plant for 24 hours? Assume there is no heat loss and the total work done is conserved.

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 (T_A) of 290 K. The engine runs at a rate of 5 cycles per second. Determine the output power of the thermal engine.

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.

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.

A flagship gasoline engine has a compression ratio of 9.6. Determine the engine's theoretical efficiency. Take the heat capacity ratio as 1.4

A typical gas-powered generator that is used in portable power applications operates on the Otto cycle model. In this type of engine, the combustion chamber is typically a single cylinder with a piston that moves up and down to complete each of the four strokes. During the compression stroke (A→B), the piston moves up, compressing the air in the cylinder. This process is adiabatic, as there is no exchange of heat between the system and its surroundings. The temperature and pressure of the air increase, and the volume decreases as the piston moves upward. The spark plug ignites (B→C) the compressed air, causing it to rapidly combust and generate heat. The volume of the cylinder remains constant. During the power stroke (C→D), the pressure decreases and pushes the piston downward. Finally, during the exhaust stroke (D→A), the exhaust gases are expelled from the cylinder through the exhaust valve due to the high pressure, while the volume remains constant. This process is isochoric. At the end of the cycle the thermodynamic state at point A returns to its initial state. The Otto cycle in a gas-powered generator is a thermodynamic process that converts the chemical energy stored in the fuel into work. Calculate the work produced in terms of temperature at points A, B, C, and D, the number of mole n, the heat capacities ratio γ, and the gas constant R.

An engine operating on the basis of the Carnot cycle is used for a certain function. The engine runs between two thermal sources with temperatures of 600 K and 400 K. In each cycle, 2500 J is transferred from the higher temperature source. Find the amount of work (W) that can be obtained from the engine per cycle.