Step 1 : Understanding the Question:
This question requires us to identify the characteristics of an ideal gas undergoing an isothermal compression. We must examine how thermodynamic variables such as temperature, pressure, volume, and internal energy interact under the specific constraints of an isothermal path, where the system is kept in thermal equilibrium with its surroundings.
Step 2 : Key Formulas and Approach:
In thermodynamics, an isothermal process is defined by constant temperature:
\[
T = \text{constant} \implies \Delta T = 0
\]
For an ideal gas, the internal energy \( U \) depends strictly on the absolute temperature:
\[
U = f(T) \implies \Delta U \propto \Delta T
\]
Using these relationships, we can determine the behavior of internal energy, work, and pressure during the compression.
Step 3 : Detailed Solution:
Note that 'isothermal' means the system is in thermal contact with a reservoir, keeping the temperature constant: \( \Delta T = 0 \).
Recall that the internal energy of an ideal gas is a function of temperature alone, represented as \( U = \frac{f}{2} n R T \).
Since the temperature change \( \Delta T \) is zero, the change in internal energy \( \Delta U \) must also be zero, meaning internal energy remains constant.
Analyze the remaining incorrect choices: compression means volume decreases, which requires work to be done on the gas (\( W<0 \)) and causes pressure to increase according to Boyle's law (\( P \propto 1/V \)).
Step 4 : Final Answer:
The correct option is (A), which states that the internal energy remains constant during the process.
\[
\boxed{\text{(A) Internal energy remains constant}}
\]