Question

The Volume of an ideal gas is 1 liter column and its Pressure is equal to $72 \mathrm{~cm}\( of \)\mathrm{Hg}$. The Volume of gas is made 900 \(\mathrm{cm}^{3}\) by compressing it isothermally. The stress of the gas will be \(\ldots \ldots \ldots \ldots .\) Hg column. (A) \(4 \mathrm{~cm}\) (B) \(6 \mathrm{~cm}\) (C) \(7 \mathrm{~cm}\) (D) \(8 \mathrm{~cm}\)

Short answer

The final pressure of the gas after isothermal compression is \(80~\text{cm Hg}\). None of the provided options (A, B, C, or D) are correct.

Step-by-step solution

Write down the given information

We are given the following information: Initial volume of the gas (V1) = 1 L Initial pressure of the gas (P1) = 72 cm of Hg Final volume of the gas (V2) = 900 cm³ Our goal is to find the final pressure of the gas (P2).

Convert volumes to the same unit

To make our calculations easier, we should convert the initial and final volumes to the same unit. We'll convert both to cm³: Initial volume (V1) = 1 L * 1000 cm³/L = 1000 cm³ Final volume (V2) = 900 cm³

Use Boyle's law to find the final pressure

Since the gas undergoes an isothermal compression, we can use Boyle's law, which states: \(P_1 V_1 = P_2 V_2\) Now, we can plug in the given values and solve for the final pressure (P2): \(P_1 V_1 = P_2 V_2\) \(72~\text{cm Hg} \times 1000~\text{cm}^3 = P_2 \times 900~\text{cm}^3\)

Solve for the final pressure (P2)

Now we can solve for P2: \(P_2 = \frac{72~\text{cm Hg} \times 1000~\text{cm}^3}{900~\text{cm}^3}\) \(P_2 = \frac{72000}{900}\) \(P_2 = 80~\text{cm Hg}\) The final pressure of the gas after isothermal compression is 80 cm of Hg. Therefore, none of the provided options (A, B, C, or D) are correct.