Correct Answer - Option 4 : 327°C
Concept:
Perfect or Ideal gas are those gases that obey the ideal gas laws that describe the basic behaviour of fluids with respect to volume, pressure, and temperature. These laws are described below:
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Gay Lussac’s Law
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It states that at constant volume, the pressure of a fixed amount of a gas varies directly with temperature.
P ∝ T ⇒ \(\frac{P}{T} = Const\)
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Boyle's Law
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For a fixed mass of gas at constant temperature, the volume is inversely proportional to the pressure or the product of pressure and the volume of a given mass of a gas is constant.
\(P\propto \frac{1}{V}\) ⇒ PV = constant
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Charle's Law
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For a fixed mass of gas at constant pressure, the volume is directly proportional to the Kelvin temperature.
\(V\propto T \ \Rightarrow \ \frac{V}{T} = Const\)
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Calculation:
Given:
V2 = 2 V1 , T1 = 27° C = 300 K and P = Const.
from Charle's Law
⇒ \( \frac{V_1}{T_1} = \frac{V_2}{T_2} \)
⇒ \( \frac{T_2}{T_1} = \frac{V_2}{V_1} = 2 \)
⇒ T2 = 2 × 300 = 600 K
⇒ T2 = 327° C
