Thermodynamics Terms

Step 1: In an adiabatic process, pressure ( ) and temperature ( ) follow the relation: where is a constant. Given that pressure is proportional to the cube of the temperature, thus, .
Step 2: The adiabatic relation between pressure and temperature for an ideal gas is given by: where is the heat capacity ratio.
Step 3: Comparing with the given relation , we equate:
Step 4: Solving for :
Step 5: Therefore, the correct answer is (D). \bigskip