A gas is heated at constant pressure from 300 K to 450 K, initial volume 2 L. Find the final volume — Physics problems | PhysLabo
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Final volume during isobaric heating

Easy 10 grade Molecular Physics and Thermodynamics / Ideal Gas
Problem statement

A gas is heated isobarically (at constant pressure) from a temperature $T_1 = 300$ K to $T_2 = 450$ K. The initial volume of the gas is $V_1 = 2$ L. Find the final volume of the gas.

Given
  • $T_1 = 300$ K
  • $T_2 = 450$ K
  • $V_1 = 2$ L
  • $V_2 = ?$
Visual demonstration
Hints
Hint 1 / 2
The pressure is constant — apply Gay-Lussac's law: $V/T = \text{const}$.
Hint 2 / 2
Always substitute the temperature in kelvins (it is already given in kelvins).
Solution

In an isobaric process the volume is directly proportional to the temperature (Gay-Lussac's law):

$$\frac{V_1}{T_1} = \frac{V_2}{T_2}$$

$$V_2 = V_1 \cdot \frac{T_2}{T_1} = 2 \cdot \frac{450}{300} = 2 \cdot 1.5 = 3 \text{ L}$$

Answer

$V_2 = 3$ L

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