Thermodynamics Terms

Step 1: Understand the process.
The process is described by the equation , where is the pressure, is the volume, and is a constant. This equation represents a polytropic process, where the exponent of is 3.

Step 2: Derive the heat capacity.
The heat capacity is given by: For a polytropic process, the relationship between pressure, volume, and temperature can be used to derive the heat capacity. The relationship for heat capacity during an expansion or compression is: Where is the adiabatic index. For a monatomic ideal gas, , which gives:
Step 3: Conclusion.
Thus, the heat capacity of the gas during the process is . Therefore, the correct answer is (3) 1.5R.

Step 1: Understand the process.
The process is described by the equation , where is the pressure, is the volume, and is a constant. This equation represents a polytropic process, where the exponent of is 3.

Step 2: Derive the heat capacity.
The heat capacity is given by: For a polytropic process, the relationship between pressure, volume, and temperature can be used to derive the heat capacity. The relationship for heat capacity during an expansion or compression is: Where is the adiabatic index. For a monatomic ideal gas, , which gives:
Step 3: Conclusion.
Thus, the heat capacity of the gas during the process is . Therefore, the correct answer is (3) 1.5R.