In one cycle, a heat engine absorbs 4400 J at 500C and exhausts 400 J. How much work does it do per cycle?
To find out how much work the heat engine does per cycle, 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:
ΔU = Q - W
Where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.
In this case, the heat engine absorbs 4400 J of heat and exhausts 400 J, so the total heat added to the system (Q) is given by:
Q = 4400 J - 400 J = 4000 J
Now, we need to find the change in internal energy (ΔU) of the heat engine. Since we are given the temperatures at which heat is absorbed (500°C) and exhausted, we can use the equation:
ΔU = n * C * ΔT
Where n is the number of moles of gas, C is the molar specific heat capacity of the gas, and ΔT is the change in temperature.
However, since we are not given the molar specific heat capacity, we need to find an alternate way to express the change in internal energy.
Let's assume that the heat engine is operating in a Carnot cycle (an idealized thermodynamic cycle). In a Carnot cycle, the thermal efficiency is given by the equation:
η = 1 - (Tc/Th)
Where η is the thermal efficiency, Tc is the temperature at which heat is exhausted, and Th is the temperature at which heat is absorbed.
We can rearrange this equation to find the work output per cycle (W):
W = Q * η = Q * (1 - (Tc/Th))
Now, let's substitute the known values into the equation:
W = 4000 J * (1 - (400°C / 500°C))
Simplifying,
W = 4000 J * (1 - 0.8) = 4000 J * 0.2 = 800 J
Therefore, the heat engine does 800 J of work per cycle.