Question

Identify the incorrect statements from the following.
I. For an adiabatic process, \( \Delta U = w_{\text{ad}} \).
II. Enthalpy is an intensive property.
III. For the process \( \text{H}_2\text{O}(\ell) \rightarrow \text{H}_2\text{O}(s) \), the entropy increases.

• A. I only
• B. I, II, III
• C. I, III only
• D. II, III only

Hint:

Intensive properties do not depend on the amount of substance, while extensive properties do. Entropy generally decreases in processes that increase order.

Answer 1

The Correct Option is D

Step 1: Analyze Statement I.
Statement I: For an adiabatic process, \( \Delta U = w_{\text{ad}} \).
In an adiabatic process, there is no heat exchange with the surroundings (\( q = 0 \)).
The first law of thermodynamics states:
$$ \Delta U = q + w $$ For an adiabatic process (\( q = 0 \)):
$$ \Delta U = w_{\text{ad}} $$ This statement is correct.
Step 2: Analyze Statement II.
Statement II: Enthalpy is an intensive property.
Enthalpy (\( H \)) is defined as:
$$ H = U + PV $$ where:
\( U \) is internal energy,
\( P \) is pressure,
\( V \) is volume.
Both internal energy (\( U \)) and the product \( PV \) are extensive properties (they depend on the amount of substance).
Therefore, enthalpy is an extensive property, not an intensive property.
This statement is incorrect.
Step 3: Analyze Statement III.
Statement III: For the process \( \text{H}_2\text{O}(\ell) \rightarrow \text{H}_2\text{O}(s) \), the entropy increases.
Entropy is a measure of disorder or randomness.
When water transitions from liquid (\( \ell \)) to solid (\( s \)), the molecules become more ordered (crystalline structure in ice).
This decrease in disorder means that the entropy decreases during this process.
This statement is incorrect.
Step 4: Identify Incorrect Statements.
From the analysis:
Statement I is correct.
Statement II is incorrect.
Statement III is incorrect.
Thus, the incorrect statements are II and III.
Final Answer: \( \boxed{\text{II, III only}} \)