Question

Which of the following statement(s) is correct for the adiabatic process?

• A. \( \binom{1}{0} \) Molar heat capacity is zero.
• B. \( \binom{1}{1} \) Molar heat capacity is infinite.
• C. \( \binom{2}{1} \) Work done on gas is equal to increase in internal energy.
• D. \( \binom{2}{0} \) The increase in temperature results in a decrease in internal energy.

Hint:

In an adiabatic process, the change in internal energy equals the negative of the work done by the system.

Answer 1

The Correct Option is C

An adiabatic process is one where no heat is exchanged with the surroundings, i.e., \( Q = 0 \). In this process, the internal energy of the system is entirely converted into work done by or on the gas. Let’s analyze each statement: A. Molar heat capacity is zero. In an adiabatic process, heat is not exchanged, so the molar heat capacity doesn't apply in the usual sense. However, this statement is not strictly true because heat capacity is a function of the process and not a direct result of adiabatic conditions. B. Molar heat capacity is infinite. This is also incorrect, as in an adiabatic process, the heat capacity is not infinite. C. Work done on gas is equal to increase in internal energy. This is the correct statement. In an adiabatic process, the work done by or on the gas is directly related to the change in internal energy. Since no heat is exchanged, the first law of thermodynamics gives \( \Delta U = -W \), where \( W \) is the work done by the gas. D. The increase in temperature results in a decrease in internal energy. This is incorrect because, in an adiabatic process, an increase in temperature generally results from the work done on the gas, leading to an increase in internal energy, not a decrease. Thus, the correct statement is \( C \), which is \( \binom{2}{1} \) Work done on gas is equal to increase in internal energy.