A perfect gas at 27°C is heated at constant pressure to 327°C. If original volume of gas at 27°C is V then volume at 327°C is

The correct option/answer is 2V.

To understand why this is correct, we can apply Charles's Law for a perfect (ideal) gas. Charles's Law states that for a given mass of an ideal gas at constant pressure, the volume is directly proportional to its absolute temperature (measured in Kelvin).

Mathematically, this relation is expressed as:
$$\frac{V_1}{T_1}=\frac{V_2}{T_2}$$
where:
• _V1 is the initial volume of the gas, which is given as V.
• _T1 is the initial absolute temperature.
• _V2 is the final volume of the gas at 327°C.
• _T2 is the final absolute temperature.

First, we must convert the temperatures from degrees Celsius (°C) to Kelvin (K) using the relation:
$$T\left(\text{K}\right)=t\left(\text{°C}\right)+273$$

Let's calculate the initial absolute temperature, _T1:
$$T_1=27+273=300\text{K}$$

Next, calculate the final absolute temperature, _T2:
$$T_2=327+273=600\text{K}$$

Now, substitute the values of _{V1 = V}, _{T1 = 300 K}, and _{T2 = 600 K} into Charles's Law:
$$\frac{V}{300}=\frac{V_2}{600}$$

Solve for the final volume _V2:
$$V_2=V\times \frac{600}{300}$$
$$V_2=2V$$
Therefore, the volume of the gas at 327°C is 2V.