Heat Engines and the Second Law of Thermodynamics Practice Problems

A freezer operating on the basis of the Carnot cycle has a constant temperature of 255 K. In each cycle, the freezer engine discards 600 J of heat in the kitchen. The kitchen has a temperature of 300 K. The freezer completes 220 cycles per minute. What is the power (P) required to maintain a constant temperature in the freezer?

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?

Consider a Carnot refrigerator that is used to maintain water cold at 5° C by rejecting heat to the atmosphere at 30 °C. In each cycle, 700 J of heat is delivered to the high-temperature reservoir. What is the coefficient of performance (K) of this refrigerator?

A gasoline engine is installed in a car to convert chemical energy into mechanical work. It operates by repeating a cycle of four stages. At each cycle, it releases 3500 J of heat while generating 1700 J of mechanical work. Determine how much heat (Q_H) should be provided to the engine at each cycle.

Data center servers are cooled by a cooling system. The cooling system works between a cold room at 5℃ and a hot room at 50℃. A 40 cm long steel bar with a diameter of 3.3 cm connects the rooms. The cooling system extracts heat from the cold room at the same rate that it is transferred through the steel bar. Compute the required power input, in watts, for the cooling mechanism to achieve this heat extraction rate. The cooling system operates on the basis of the Carnot cycle and the thermal conductivity of steel is 45 W/m•K.

A cooling unit operates with a Carnot cycle between -15°C and 30°C. Find how much (i) heat is dissipated into the surrounding environment and (ii) energy must be supplied to the cooling unit in order to bring 18 kg of a liquid substance from 30°C to its solidification point at 5°C. Its latent heat of fusion (L_f) is 2.34 × 10⁵ J/kg.

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.

In the combined system in which a Carnot heat engine powers a Carnot refrigerator, the heat absorbed from the hot reservoir Q₁ is 1200 J. The hot reservoir has a temperature of 800 K, while the cold reservoir has a temperature of 500 K as shown in the figure. Determine the heat transfer values Q₃ and Q₄ for this interconnected arrangement.

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.

What is the efficiency of a steam engine that expels 9000 J of heat while performing 3000 J of work?

A nuclear power station generates 770 MW of electrical energy. If the efficiency of the power station is 36%, calculate the amount of heat energy discharged per second.

A certain power plant operates with a thermal energy source at an initial temperature of approximately 600 °C and it possesses an ideal Carnot efficiency of roughly 25%. Now if we were to increase this particular ideal efficiency to roughly 50%, then what would be the required value for thermal energy source of this particular power plant?

A factory conveyor belt system uses a four-motor setup, with each motor operating with an efficiency of 0.28 and delivering 190 J of work per cycle. Calculate the total work done by the conveyor belt system in one second if each motor runs at 28 cycles per second.

A scientist wants to design an engine that uses the temperature difference between desert sand during daytime hours which are a temperature of 47 °C and the nighttime hours that are a temperature of -3 °C. What could be the highest possible efficiency value of this particular engine be?

Geothermal energy is a form of renewable energy that harnesses the heat from the Earth's interior. In certain regions, geothermal reservoirs can have temperatures ranging from 150°C to 370°C. Why might a geothermal power plant be feasible despite having a relatively low efficiency?

A mountaineer weighing around 75 kg consumes about 5.0 x 10³ kcal of food energy per day in order to maintain his metabolism which is equal to Q_H. Imagine he acts like an isolated heat engine that operates between his body temperature of approximately 37°C and an ambient temperature of -5.0°C. What would be his potential altitude gain in one day using only this particular amount of energy?

Imagine an air conditioner with an elliptical machine attachment that lets you do the work rather than using electricity from the power grid of your home. The air conditioner has a coefficient of performance of 4, and you can exercise at an energy output rate of about 150 watts for 45 minutes. Find the amount of heat transferred to the air conditioner. Give the answer in kWh.

A truck does work at a rate of 9 kJ/s when traveling at a constant speed of 25 m/s on a level road, expending energy to overcome friction. The truck can travel 15 km on 1.0 L of diesel, which provides 4.0 × 10⁷ J of energy. Given that the surrounding temperature (T _L) is 35°C, calculate the value for the minimum temperature (T_H) of the engine of the truck during operation.

Consider an eight-cylinder petrol engine delivering an output power of about 0.28 kJ/cycle/cylinder at a speed rate of about 30 revolutions every second (1800 rpm) at an efficiency of 0.35. What is the amount of heat energy supplied by petrol every second?