Question

In which of the following process involving an ideal gas, the change in internal energy and the change in enthalpy would be zero?

• A. Isobaric process
• B. Isothermal process
• C. Adiabatic process
• D. Polytropic process

Hint:

In an isothermal process, the temperature is constant, and hence there is no change in internal energy or enthalpy for an ideal gas.

Answer 1

The Correct Option is B

Step 1: Understanding the isothermal process. 
An isothermal process is one where the temperature of the system remains constant throughout the process. For an ideal gas, internal energy (\( U \)) and enthalpy (\( H \)) are both functions of temperature. Since the temperature remains constant during an isothermal process, there is no change in the internal energy (\( \Delta U = 0 \)).
The enthalpy (\( H \)) of an ideal gas also depends on temperature, and since the temperature is constant, there is no change in enthalpy (\( \Delta H = 0 \)). \[ \Delta U = 0 \quad \text{and} \quad \Delta H = 0 \quad \text{(for an isothermal process)}. \] 
Step 2: Understanding other processes. 
Isobaric process: The process occurs at constant pressure. There is a change in enthalpy since enthalpy is related to both temperature and pressure.
Adiabatic process: The process occurs without heat exchange with the surroundings. There is a change in internal energy, as energy is exchanged in the form of work.
Polytropic process: The process follows a polytropic relation between pressure and volume, which typically involves changes in both internal energy and enthalpy.
Step 3: Conclusion. 
In an isothermal process, the internal energy and enthalpy do not change because the temperature is constant. 
Final Answer: The change in internal energy and enthalpy would be zero in an isothermal process.