P2\(\therefore \frac{{{V_1}}}{{{T_1}}} = \frac{{{V_2}}}{{{T_2}}}\)\(\RIGHTARROW \frac{{{V_2}}}{{{V_1}}} = \frac{{{T_2}}}{{{T_1}}}\)\(\Rightarrow \frac{{{V_2}}}{{{V_1}}} = \frac{3}{4}\)For process 2 – 3: V2 = V3\(\therefore \frac{{{V_3}}}{{{V_2}}} = 1\)Now, \(\frac{{{V_3}}}{{{V_1}}} = \frac{{{V_3}}}{{{V_2}}} \times \frac{{{V_2}}}{{{V_1}}} = 1 \times \frac{3}{4} = \frac{3}{4}\) \(\Rightarrow \frac{{{V_3}}}{{{V_1}}} = 0.75\)

"> P2\(\therefore \frac{{{V_1}}}{{{T_1}}} = \frac{{{V_2}}}{{{T_2}}}\)\(\RIGHTARROW \frac{{{V_2}}}{{{V_1}}} = \frac{{{T_2}}}{{{T_1}}}\)\(\Rightarrow \frac{{{V_2}}}{{{V_1}}} = \frac{3}{4}\)For process 2 – 3: V2 = V3\(\therefore \frac{{{V_3}}}{{{V_2}}} = 1\)Now, \(\frac{{{V_3}}}{{{V_1}}} = \frac{{{V_3}}}{{{V_2}}} \times \frac{{{V_2}}}{{{V_1}}} = 1 \times \frac{3}{4} = \frac{3}{4}\) \(\Rightarrow \frac{{{V_3}}}{{{V_1}}} = 0.75\)

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A certain amount of an ideal gas initially at a pressure P1 and temperature T1. First, it undergoes a constant pressure process 1 – 2 such that T2 = 3T1/4. Then, it undergoes a constant volume process 2 – 3 such that T3 = T1/2. The ratio of the final volume to the initial volume of the ideal gas is

Fluid Mechanics First Law Thermodynamics in Fluid Mechanics . 7 months ago

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Concept:For process 1 – 2 : P1 = P2\(\therefore \frac{{{V_1}}}{{{T_1}}} = \frac{{{V_2}}}{{{T_2}}}\)\(\RIGHTARROW \frac{{{V_2}}}{{{V_1}}} = \frac{{{T_2}}}{{{T_1}}}\)\(\Rightarrow \frac{{{V_2}}}{{{V_1}}} = \frac{3}{4}\)For process 2 – 3: V2 = V3\(\therefore \frac{{{V_3}}}{{{V_2}}} = 1\)Now, \(\frac{{{V_3}}}{{{V_1}}} = \frac{{{V_3}}}{{{V_2}}} \times \frac{{{V_2}}}{{{V_1}}} = 1 \times \frac{3}{4} = \frac{3}{4}\) \(\Rightarrow \frac{{{V_3}}}{{{V_1}}} = 0.75\)

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Posted on 26 Nov 2024, this text provides information on Fluid Mechanics related to First Law Thermodynamics in Fluid Mechanics. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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