A gas is filled in a vessel at a certain temperature and at a pressure of `80 cm` of Hg. At the same temperature, more gas is filled in the vessel so that its mean increases by `60%`. Determine the resultant in the vessel.

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Understand the initial conditions
We have a gas in a vessel at a pressure \( P_1 = 80 \, \text{cm of Hg} \) and at a constant temperature.

### Step 2: Determine the increase in mass
The problem states that more gas is filled in the vessel such that the mass increases by \( 60\% \). If we denote the initial mass of the gas as \( M_1 = M \), then the new mass of the gas after filling more gas is:
\[ M_2 = M_1 + 0.6M_1 = 1.6M_1 = 1.6M \]

### Step 3: Relate pressure to mass
At constant temperature and volume, the pressure of a gas is directly proportional to its mass. Thus, we can write:
\[ \frac{P_1}{P_2} = \frac{M_1}{M_2} \]
From this, we can express \( P_2 \):
\[ P_2 = P_1 \cdot \frac{M_2}{M_1} \]

### Step 4: Substitute known values
Now, substituting the known values into the equation:
\[ P_2 = 80 \, \text{cm of Hg} \cdot \frac{1.6M}{M} \]
The \( M \) cancels out:
\[ P_2 = 80 \, \text{cm of Hg} \cdot 1.6 \]

### Step 5: Calculate the resultant pressure
Now, performing the multiplication:
\[ P_2 = 80 \cdot 1.6 = 128 \, \text{cm of Hg} \]

### Final Answer
The resultant pressure in the vessel after filling more gas is:
\[ \boxed{128 \, \text{cm of Hg}} \]

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