The Specific heat of a gas in an isothermal Process is (A) zero (B) Negative (C) Infinite (D) Remairs

In an isothermal process, the temperature of the gas remains constant throughout the process. Since there is no change in temperature, there should be no change in the internal energy of the gas. This is because the internal energy of an ideal gas depends only on its temperature.

Specific heat is a measure of the amount of heat required to raise the temperature of a given mass of a substance by 1 degree Celsius (or 1 Kelvin). It is denoted by 'c' and mathematically defined as: \(c = \frac{q}{m \Delta T}\) where: - c = specific heat, - q = amount of heat added to or removed from the substance, - m = mass of the substance, - ΔT = change in temperature.

Now, let's evaluate each option in light of our understanding of the isothermal process and specific heat: (A) zero: If the specific heat is zero, it implies that no heat is required to change the temperature of the gas. However, since the temperature remains constant in an isothermal process, we cannot rule out this option. (B) Negative: A negative specific heat means that the temperature would decrease while heat is being added or that the temperature would increase while heat is being removed, which is not applicable in an isothermal process. (C) Infinite: An infinite specific heat implies that an infinite amount of heat is required to change the temperature of the gas, even by a small amount. Since there is no change in temperature during an isothermal process, it means that an infinite amount of heat must be involved in order to maintain the constant temperature. (D) Remains constant: This is not a valid response to the question.

Based on our evaluation, we can conclude that the specific heat of a gas in an isothermal process is infinite (C). This is because an infinite amount of heat must be involved in order to maintain a constant temperature throughout an isothermal process.