The graph of PV vs P for a gas is

Options

A. parabolic
B. hyperbolic
C. a straight line parallel to X-axis
D. a straight line passing through origin

Answer

To solve the question regarding the graph of PV vs P for a gas, we will follow these steps:

### Step 1: Understand the relationship between PV and P
According to Boyle's Law, for a given amount of gas at constant temperature, the product of pressure (P) and volume (V) is a constant. This means that PV = constant.

### Step 2: Rearranging the equation
If we consider the relationship PV = constant, we can express this as:
\[ PV = k \]
where \( k \) is a constant.

### Step 3: Analyzing the graph of PV vs P
When we plot PV against P, we are essentially plotting a constant value against varying pressure. Since PV is constant, the graph of PV vs P will not change with varying P.

### Step 4: Determine the shape of the graph
Since PV is constant, the graph of PV vs P will be a horizontal line. This is because for any value of P, the value of PV remains the same, leading to a straight line parallel to the x-axis.

### Step 5: Conclusion
From our analysis, we conclude that the graph of PV vs P for a gas is a straight line parallel to the x-axis.

### Final Answer
The correct option is: **A straight line parallel to the x-axis.**

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