In an isothermal process, the temperature of the system remains constant. For an ideal gas, the internal energy is a function of temperature alone. Therefore, during an isothermal change, the internal energy of an ideal gas does not change.
This means that if the system undergoes an isothermal process, the change in internal energy (ΔU) is equal to zero:
\[ \Delta U = 0 \quad \text{(for an ideal gas in isothermal process)} \]
Since there is no change in internal energy, any heat (Q) added to the system is entirely converted into work (W) done by or on the system, according to the first law of thermodynamics:
\[ \Delta U = Q - W \]
So, for an isothermal process involving an ideal gas:
\[ 0 = Q - W \quad \Rightarrow \quad Q = W \]
In summary, during an isothermal change for an ideal gas, the internal energy remains constant, and any heat added or removed from the system results in equal work done.
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