••••••••••air is filled at 60°c in a vessel of open mouth the vessel is heated with a temperature t so that 1/4th part of air escapes.assuming the volume of vessel remaining constant,the value of T is
if the volume is not 5/4 (including the 1/4 that escaped), then temp has to be 5/4 original temp (in Kelvins)
PV=nRT
To find the value of T, we need to understand the concept of Charles' Law and the behavior of gases.
According to Charles' Law, at constant pressure, the volume of a gas is directly proportional to its absolute temperature. This can be expressed as:
V₁ / T₁ = V₂ / T₂
where V₁ and T₁ are the initial volume and temperature, and V₂ and T₂ are the final volume and temperature.
In this problem, the volume of the vessel remains constant, so we can simplify the equation as:
T₁ / T₂ = V₁ / V₂
Initially, the vessel is filled with air at a temperature of 60°C, which needs to be converted to Kelvin (K) for the equation:
T₁ = 273 + 60 = 333 K
Let's assume the final temperature after heating is T.
Since 1/4th part of the air escapes, the remaining 3/4th part of the air is still in the vessel. Therefore, the final volume (V₂) would be 3/4th of the initial volume (V₁).
Now we can plug in the values into the equation:
333 / T = (3/4) / 1
Cross multiplying:
333 = (3/4)T
Dividing both sides by (3/4):
T = (333 * 4) / 3
T ≈ 444 K
Therefore, the value of T is approximately 444 Kelvin.