Question

For a free expansion of an ideal gas in an isolated chamber which of the following statements is true?

• A. (a) Positive work is done by the system.
• B. (b) The entropy of the system increases.
• C. (c) The temperature of the system decreases.
• D. (d) The internal energy of the system decreases.

Answer 1

The correct option is B

(b) The entropy of the system increases.

Explanation for correct option:

Option (B): The entropy of the system increases

According to the second law of thermodynamics, the system's entropy tends to increase for a free expansion of an ideal gas in an isolated chamber.

$\Rightarrow ∆S>0$

Therefore, the Entropy of the system increases.

Explanation for incorrect options:

Option (A): Positive work is done by the system

Work done by the gas is zero since there is no external pressure applied to the system.

Option (C): The temperature of the system decreases

Because internal energy in an ideal gas solely depends on kinetic energy, which is proportional to temperature, it is claimed that there is no overall change in temperature.

Option (D): The internal energy of the system decreases.

Step 1: Finding heat absorbed or released:

Since the process is adiabatic, neither heat is released nor absorbed.
$\Rightarrow ∆Q=0$

Step 2: Finding Work done by gas:
Here, the gas expands freely without any External Pressure.
So, Work done by gas = 0

Step 3: Finding internal energy:
By the first Law of thermodynamics:
$∆E=∆Q+W\Rightarrow 0+0=0$
So, the change in internal energy is zero

Thus, option (B) is correct; for a free expansion of an ideal gas in an isolated chamber, the system's entropy increases.