Question

A balloon containing an ideal gas is initially kept in an evacuated and insulated room. If the balloon ruptures and the gas fills the entire room, what is the correct statement at the end of the process?

• A. The internal energy of the gas decreases from its initial value, but the enthalpy remains constant
• B. The internal energy of the gas increases from its initial value, but the enthalpy remains constant
• C. Internal energy and enthalpy of the gas remain constant
• D. Internal energy and enthalpy of the gas increase

Hint:

Free expansion of an ideal gas is simultaneously isothermal ($T = \text{constant}$), isenuclic/isothermal-internal-energy ($U = \text{constant}$), and isenthalpic ($H = \text{constant}$). However, it is highly irreversible, so entropy increases ($\Delta S \gt 0$).

Answer 1

The Correct Option is C

To solve this problem, we need to understand the thermodynamic process involved when a balloon containing an ideal gas is ruptured in an evacuated and insulated room.

Initially, the balloon contains an ideal gas at specific pressure and volume, and the room is evacuated, meaning there is no other gas present. The room being insulated implies that there is no heat exchange with the surroundings.

1. System Description:
   • The balloon is a flexible, thin-walled container holding the gas.
   • The process starts with the balloon intact and ends when the gas fills the entire room after the balloon ruptures.
2. Type of Process:
   • This is a classic example of a free expansion process characterized by:
     • No work is done because the gas is expanding freely into a vacuum.
     • No heat exchange with the surroundings because the system is insulated.
3. Thermodynamic Analysis:
   • During a free expansion of an ideal gas in an insulated system:
     • The work done on or by the system is zero.
     • The first law of thermodynamics states Q = ΔU + W.
     • In this case, Q = 0 and W = 0, thus making ΔU = 0.
     • This means the internal energy of the gas remains constant.
   • Additionally, for an ideal gas, the internal energy is only a function of temperature. Since the internal energy remains constant, the temperature does not change, and hence the enthalpy, which is a function of temperature, also remains constant.
4. Conclusion:
   • Since both internal energy and enthalpy remain constant during this free expansion process, the correct answer is: "Internal energy and enthalpy of the gas remain constant."