Liquid oxygen at `50 K` is heated to `300 K` at constant pressure of `1 atm`. The rate of heating is constant. Which of the following graphs represents the variation of temperature with time?

Options

A.
B.
C.
D.

Explanation

To solve the problem, we need to analyze the heating process of liquid oxygen as it transitions from a liquid state at 50 K to a gaseous state at 300 K under constant pressure. Here’s a step-by-step breakdown of the process:

### Step 1: Understand the Initial Condition
- The liquid oxygen starts at a temperature of 50 K.

### Step 2: Heating the Liquid
- As we begin to heat the liquid oxygen, its temperature will rise. The rate of heating is constant, meaning that the temperature will increase linearly with time until it reaches the boiling point of oxygen.

### Step 3: Identify the Boiling Point
- The boiling point of oxygen is approximately 90 K. As the temperature approaches this point, the liquid will begin to boil.

### Step 4: Phase Change
- During the phase change from liquid to gas (boiling), the temperature remains constant at the boiling point (90 K) until all the liquid has converted to gas. This is because the heat energy added during this phase change is used to overcome the latent heat of vaporization rather than increasing the temperature.

### Step 5: Heating the Gas
- Once all the liquid has turned into gas, the temperature of the gaseous oxygen will start to increase again. This increase in temperature will continue until it reaches 300 K.

### Step 6: Graphical Representation
- The graph representing the temperature vs. time will show a linear increase in temperature from 50 K to 90 K, followed by a horizontal line (constant temperature) at 90 K during the boiling phase, and finally another linear increase from 90 K to 300 K.

### Conclusion
- The correct graph will show an initial linear increase, a plateau at the boiling point, and then another linear increase.