Question

For the following change: H$_2$O(l) $\rightarrow$ H$_2$O(g)
5$^\circ$C $\rightarrow$ 100$^\circ$C
Select the correct answer

• A. q = +ve, w = +ve, $\Delta$U = +ve
• B. q = -ve, w = -ve, $\Delta$U = +ve
• C. q = +ve, w = -ve, $\Delta$U = +ve
• D. q = -ve, w = -ve, $\Delta$U = -ve

Hint:

For phase changes such as evaporation, heat is added to the system (q = +ve), and the system does work on the surroundings (w = -ve). The internal energy increases as a result.

Answer 1

The Correct Option is C

Step 1: Understanding the process.
This process represents the phase transition of water from liquid to gas, known as evaporation. The process occurs at constant temperature, so the temperature change is zero. However, there is heat added to the system for the phase change to occur.
Step 2: Determine the heat flow (q).
Since water is converting from liquid to gas, energy must be supplied to the system, meaning that heat is absorbed. Hence, q = +ve.
Step 3: Work (w).
During the transition from liquid to gas, the volume of water increases as it turns into vapor. This expansion against the atmospheric pressure means that work is done by the system. Hence, w = -ve (work is done by the system on the surroundings).
Step 4: Change in internal energy ($\Delta$U).
The increase in heat results in an increase in the internal energy of the system, so $\Delta$U = +ve.
Step 5: Conclusion.
The correct answer is (3) q = +ve, w = -ve, $\Delta$U = +ve.