\( \binom{1}{1} \) Molar heat capacity is infinite.
\( \binom{2}{1} \) Work done on gas is equal to increase in internal energy.
\( \binom{2}{0} \) The increase in temperature results in a decrease in internal energy.
Show Solution
The Correct Option isC
Solution and Explanation
An adiabatic process is defined by the absence of heat exchange with the surroundings, meaning \( Q = 0 \). During such a process, the system's internal energy is entirely transformed into work performed by or on the gas.
Let's evaluate each assertion:
A. Molar heat capacity is zero.
While heat exchange is absent in an adiabatic process, rendering the typical definition of molar heat capacity inapplicable, this statement is not entirely accurate. Heat capacity is process-dependent and not a direct consequence of adiabatic conditions.
B. Molar heat capacity is infinite.
This statement is also erroneous; the heat capacity in an adiabatic process is not infinite.
C. Work done on gas is equal to increase in internal energy.
This statement is accurate. In an adiabatic process, the work performed by or on the gas directly correlates with the change in internal energy. Given that no heat is exchanged, the first law of thermodynamics dictates \( \Delta U = -W \), where \( W \) represents the work done by the gas.
D. The increase in temperature results in a decrease in internal energy.
This is incorrect. In an adiabatic process, an elevated temperature typically arises from work performed on the gas, which results in an increase, not a decrease, in internal energy.
Therefore, the correct statement is C: \( \binom{2}{1} \) Work done on gas is equal to increase in internal energy.
