600 cc of a gas at a pressure of 750 mm is compressed to 500 cc. Taking the temperature to remain constant, the increase in pressure is

Options

A. 150 mm
B. 250 mm
C. 350 mm
D. 450 mm

Explanation

To solve the problem step by step, we can use Boyle's Law, which states that for a given mass of gas at constant temperature, the product of pressure and volume is constant. This can be expressed as:

\[ P_1 V_1 = P_2 V_2 \]

### Step 1: Identify the given values
- Initial volume \( V_1 = 600 \, \text{cc} \)
- Initial pressure \( P_1 = 750 \, \text{mm} \)
- Final volume \( V_2 = 500 \, \text{cc} \)

### Step 2: Apply Boyle's Law
Using Boyle's Law, we can express the relationship between the initial and final states of the gas:

\[ P_1 V_1 = P_2 V_2 \]

### Step 3: Rearrange the equation to solve for \( P_2 \)
We need to find the final pressure \( P_2 \). Rearranging the equation gives us:

\[ P_2 = \frac{P_1 V_1}{V_2} \]

### Step 4: Substitute the known values into the equation
Now, substitute the known values into the equation:

\[ P_2 = \frac{750 \, \text{mm} \times 600 \, \text{cc}}{500 \, \text{cc}} \]

### Step 5: Calculate \( P_2 \)
Now, perform the calculation:

\[ P_2 = \frac{750 \times 600}{500} \]
\[ P_2 = \frac{450000}{500} \]
\[ P_2 = 900 \, \text{mm} \]

### Step 6: Calculate the increase in pressure
Now, we can find the increase in pressure by subtracting the initial pressure from the final pressure:

\[ \text{Increase in pressure} = P_2 - P_1 \]
\[ \text{Increase in pressure} = 900 \, \text{mm} - 750 \, \text{mm} \]
\[ \text{Increase in pressure} = 150 \, \text{mm} \]

### Conclusion
The increase in pressure is \( 150 \, \text{mm} \).

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