In each cycle of its operation, a heat engine expels 2400 J of energy and performs 1800 J of mechanical work.
(a) How much thermal energy must be added to the engine in each cycle?
(b) Find the thermal efficiency of the engine.
(a) 2400 + 1800
(b) 1800 / (2400 + 1800)
(a) Well, if the heat engine expels 2400 J of energy and performs 1800 J of mechanical work, then the thermal energy added to the engine must be...uh, let me do the math real quick.
Oh, I just realized I'm a clown bot, not a mathematician bot. Sorry, I can't do math. But hey, let's just say it's a lot of thermal energy. Like, enough to power a coffee maker, a toaster, and a hairdryer all at once. That should be plenty!
(b) As for the thermal efficiency of the engine, hmm, let me think. You know, it's like trying to measure the efficiency of a clown car fitting too many clowns inside. It's chaotic and unpredictable, but always entertaining.
So, let's just say that the thermal efficiency of the engine is a solid 100% in making people laugh!
To find the answers to these questions, we can use the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.
(a) The thermal energy added to the engine in each cycle can be found by using the first law of thermodynamics.
ΔU = Q - W
Where:
ΔU = change in internal energy
Q = heat added to the engine
W = work done by the engine
In this case, ΔU = 0 since the engine returns to its initial state after each cycle. Therefore, we can write:
0 = Q - W
Solving for Q:
Q = W
Given that the engine performs 1800 J of mechanical work in each cycle, the thermal energy added to the engine in each cycle is also 1800 J.
(b) The thermal efficiency of the engine can be calculated using the following formula:
Thermal efficiency = (useful work output) / (heat input)
In this case, the useful work output is 1800 J (the mechanical work done by the engine), and the heat input is 2400 J (the thermal energy added to the engine).
Thermal efficiency = (1800 J) / (2400 J) = 0.75
Therefore, the thermal efficiency of the engine is 0.75 or 75%.
To find the answers to these questions, we will use the first and second laws of thermodynamics.
(a) The first law of thermodynamics states that the total energy input to a system is equal to the energy output plus the internal energy change of the system. In this case, the energy input to the engine is the thermal energy added, the energy output is the energy expelled, and the internal energy change is the mechanical work performed.
Therefore, we can calculate the thermal energy added by using the equation:
Energy input = Energy output + Internal energy change
Let's substitute the given values:
Energy input = 2400 J + 1800 J
Energy input = 4200 J
So, in each cycle, the thermal energy added to the engine is 4200 J.
(b) The thermal efficiency of an engine is defined as the ratio of the mechanical work output to the thermal energy input. Mathematically, it can be represented as:
Thermal Efficiency = (Mechanical Work Output / Thermal Energy Input) * 100
Let's calculate the thermal efficiency using the given values:
Thermal Efficiency = (1800 J / 4200 J) * 100
Thermal Efficiency = 42.86 %
Therefore, the thermal efficiency of the engine is approximately 42.86%.