Final answer:
The specific heat of a gas during an isothermal process is considered to be infinite because the temperature remains constant, and no amount of heat transfer results in a change in temperature.
Step-by-step explanation:
The specific heat of a gas in an isothermal process is infinite. In an isothermal process, the temperature of the gas remains constant by definition. Due to the first law of thermodynamics, for an ideal monatomic gas undergoing an isothermal process, the change in internal energy (ΔU) is zero since ΔU = Q - W (where Q is the net heat transfer into the gas and W is the work done by the gas).
Because there is no change in internal energy, and because temperature remains constant, the specific heat, which is the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius, can be considered infinite. This is because, no matter how much heat is added, the temperature does not change in an isothermal process.