To understand how a temperature-vs.-time graph is interpreted, consider the various phases and changes matter can undergo when heat is added or removed. Here is a step-by-step explanation of each option:
1. Option A: A horizontal line shows that the temperature increases at a constant rate over time.
- This statement is incorrect. In a temperature-vs.-time graph, a horizontal line represents a period where the temperature remains constant over time, not where it increases. This typically happens during a phase change, such as the melting of ice or boiling of water.
2. Option B: A vertical line shows that the temperature decreases at a constant rate over time.
- This statement is also incorrect. A vertical line on a temperature-vs.-time graph would imply an instantaneous change in temperature, which is not realistic for regular physical processes. Temperature changes over time are represented by sloped lines, not vertical ones.
3. Option C: Horizontal lines where the temperature is constant during phase changes connect upward-sloping lines where the temperature increases.
- This is the correct statement. During a phase change (e.g., melting of ice, boiling of water), the temperature remains constant despite the input of heat energy. Thus, the graph has horizontal lines during these phase changes. Outside of phase changes, the temperature of the substance increases with time if heat is continually added, represented by upward-sloping lines.
4. Option D: Horizontal lines where the temperature increases are connected by upward-sloping lines where the temperature is constant for each phase.
- This statement is incorrect. It incorrectly describes both the nature of horizontal lines and the behavior of temperature during phase changes. Horizontal lines represent constant temperature (not increasing temperature), and upward-sloping lines represent increases in temperature (not constant temperature).
The correct statement that accurately describes the appearance of a temperature-vs.-time graph is:
Option C: Horizontal lines where the temperature is constant during phase changes connect upward-sloping lines where the temperature increases.
In summary, a temperature-vs.-time graph shows horizontal lines during phase changes (indicating constant temperature) and upward-sloping lines where the temperature increases over time. Therefore, the correct answer is Option C.
