The volume of a certain mass of gas at `N.T.P.` is `27.5 cm^(3)`. What pressure will be necessary to keep the volume same at `27^(@)C`?

Explanation

To solve the problem, we will use the ideal gas law, which states that for a given mass of gas, the ratio of pressure (P), volume (V), and temperature (T) remains constant. The relationship can be expressed as:

\[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \]

### Step 1: Identify the known values
- Volume at NTP (V1) = 27.5 cm³
- Volume at 27°C (V2) = 27.5 cm³ (same as V1)
- Pressure at NTP (P1) = 1.013 bar
- Temperature at NTP (T1) = 273 K (converted from 0°C)
- Temperature at 27°C (T2) = 27 + 273 = 300 K

### Step 2: Write down the ideal gas equation
Using the ideal gas equation, we can set up the relationship:

\[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \]

### Step 3: Rearrange the equation to solve for P2
Since V1 = V2, we can simplify the equation to:

\[ P_1 \cdot \frac{1}{T_1} = P_2 \cdot \frac{1}{T_2} \]

Rearranging gives:

\[ P_2 = P_1 \cdot \frac{T_2}{T_1} \]

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

\[ P_2 = 1.013 \, \text{bar} \cdot \frac{300 \, \text{K}}{273 \, \text{K}} \]

### Step 5: Calculate P2
Now, perform the calculation:

\[ P_2 = 1.013 \cdot \frac{300}{273} \approx 1.113 \, \text{bar} \]

### Final Answer
The pressure necessary to keep the volume the same at 27°C is approximately **1.113 bar**.

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