Thermodynamics: Practice Problem & Solution
Equal masses of an ideal gas are sealed in two vessels one of pressure \(P_0\) and other of pressure \(2P_0\). If first vessel is at temperature of 400 K and the other is at 600 K. Find the ratio of volume of two container.
Solution Explained:
To solve this problem, we apply the core principles of Thermodynamics. Understanding the underlying formula is key to arriving at the correct answer below:
From the ideal gas law \(PV = nRT\), the volume is proportional to \(\frac{T}{P}\) for equal masses of the same gas. Thus, \(\frac{V_1}{V_2} = \frac{T_1}{T_2} \times \frac{P_2}{P_1} = \frac{400}{600} \times \frac{2P_0}{P_0} = \frac{4}{3}\).
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