An ideal gas performs 453 of work and loses 45J of internal energy
To understand the relationship between work and internal energy for an ideal gas, we can make use of the First Law of Thermodynamics, also known as the Law of Energy Conservation. According to this law, the change in internal energy (ΔU) of a system is equal to the heat transferred (Q) into the system minus the work done (W) by the system:
ΔU = Q - W
In your case, the ideal gas performs 453 J of work and loses 45 J of internal energy. This means that the work done by the gas (W) is 453 J (positive value because work is being done by the gas) and the change in internal energy (ΔU) is -45 J (negative value because the internal energy is decreasing). Plugging these values into the equation, we get:
-45 J = Q - 453 J
To find the heat transferred (Q), we need to isolate it on one side of the equation. Adding 453 J to both sides, we have:
-45 J + 453 J = Q - 453 J + 453 J
408 J = Q
Therefore, the heat transferred into the gas is 408 J.
To summarize:
- Work done by the ideal gas (W) = 453 J
- Change in internal energy (ΔU) = -45 J
- Heat transferred into the gas (Q) = 408 J