The volume of an ideal gas is 1 litre and its pressure is equal to 72 cm of mercury column. The volume of gas is made 900 cm 3 by compressing it isothermally. The stress of the gas will be

Options

A. 8 cm (mercury)
B. 7 cm(mercury)
C. 6 cm (mercury)
D. 4 cm(mercury)

Answer

To solve the problem step by step, we will use the ideal gas law and the concept of isothermal processes.

### Step 1: Convert the initial volume and pressure to consistent units
The initial volume \( V_1 \) is given as 1 liter. We need to convert this to cubic centimeters (cm³):
\[ V_1 = 1 \text{ liter} = 1000 \text{ cm}^3 \]
The initial pressure \( P_1 \) is given as 72 cm of mercury. We can convert this to pascals (Pa) using the relation:
\[ P_1 = 72 \text{ cm} \times \rho_{Hg} \times g \]
Where \( \rho_{Hg} \) is the density of mercury (approximately \( 13,600 \text{ kg/m}^3 \)) and \( g \) is the acceleration due to gravity (approximately \( 9.81 \text{ m/s}^2 \)). However, for our calculations, we will keep it in cm of mercury for simplicity.

### Step 2: Identify the final volume
The final volume \( V_2 \) after isothermal compression is given as:
\[ V_2 = 900 \text{ cm}^3 \]

### Step 3: Use the isothermal condition
For an isothermal process, we can use the relation:
\[ P_1 V_1 = P_2 V_2 \]
We need to find the final pressure \( P_2 \).

### Step 4: Rearranging the equation to find \( P_2 \)
Rearranging the equation gives:
\[ P_2 = \frac{P_1 V_1}{V_2} \]

### Step 5: Substitute the known values
Substituting the known values into the equation:
\[ P_2 = \frac{72 \text{ cm} \times 1000 \text{ cm}^3}{900 \text{ cm}^3} \]

### Step 6: Calculate \( P_2 \)
Now, calculating \( P_2 \):
\[ P_2 = \frac{72000 \text{ cm}}{900} = 80 \text{ cm of mercury} \]

### Final Answer
Thus, the stress (pressure) of the gas after isothermal compression is:
\[ P_2 = 80 \text{ cm of mercury} \]