Question

An ideal monoatomic gas initially at 300 K expands adiabatically into a vacuum to double its volume. The final temperature of the gas is: a) 150 K b) 200 K c) 300 K d) 600 K

Answer 1

The final temperature of an ideal monoatomic gas expanding adiabatically into a vacuum to double its volume remains constant at 300 K, since in a free expansion, no work is done and no heat is transferred. The correct answer is C.

Step-by-step explanation:

The question involves determining the final temperature of an ideal monoatomic gas that expands adiabatically into a vacuum to double its volume. The initial temperature is given as 300 K. In adiabatic expansion where no heat is transferred to or from a system, the temperature change of the gas can be calculated using the adiabatic process equation for an ideal gas. However, it is crucial to note that when a gas expands into a vacuum, this process is called a free expansion, and no work is done on or by the gas since the external pressure is zero.

In a free expansion, there is no change in the internal energy of the gas because no work is done and no heat is transferred; as a result, the temperature of an ideal gas remains constant. Therefore, in this specific scenario, the final temperature of the gas is the same as the initial temperature, which is c) 300 K.