An open vessel at ${27}^{0}C$  is heated until three-fourths mass of the air in it has been expelled. Neglecting the expansion of the vessel, the temperature to which the vessel has been heated is

Option A) is Correct.
Initial Conditions: We have a mass of gas at an initial temperature of 27°C. Let's denote the initial amount of gas as n moles.

Heating Process: Upon heating, 3/4 of the gas is expelled. The remaining amount of gas is therefore n - 3n/4 = n/4 moles.

Applying the Ideal Gas Law: The Ideal Gas Law in this scenario relates the initial and final states of the gas. The law is given by n₁T₁ = n₂T₂, where n₁ and n₂ are the initial and final amounts of gas, and T₁ and T₂ are the initial and final temperatures.

• Initial state (n₁, T₁): n₁ = n moles, T₁ = 27°C which is 300 Kelvin.
• Final state (n₂, T₂): n₂ = n/4 moles, T₂ = T (the final temperature we want to find).

Substituting and Solving for T: Substituting these into the Ideal Gas Law equation:

n x 300 = n/4 x T

Simplifying this, we get:

T = 4 x n x 300 / n = 1200 K

Thus, the final temperature T after expelling 3/4 of the gas is 1200 Kelvin, which is equivalent to 926.85°C.