Solving 1.5 Moles Monatomic Ideal Gas at 314K - No Calc

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The discussion revolves around calculating the heat removed from 1.5 moles of a monatomic ideal gas during isothermal compression from 3 m³ to 1 m³ at 314K. It highlights that the change in internal energy (delta U) is zero for an isothermal process, leading to the relationship Q = -W, where Q is heat and W is work done on the gas. Participants express frustration over the inability to solve the problem without calculus, noting that algebra-based textbooks often reference calculus for justification. The consensus is that a solution requires understanding the area under the P-V curve, which cannot be achieved without calculus. Ultimately, the discussion emphasizes the limitations of algebraic methods in solving thermodynamic problems involving ideal gases.
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1. 1.5 moles of a monatomic ideal gas is enclosed at 314K. THe initial volume of the gas is 3m^3. The gas is comperssed isothermally to a final volume of 1m^3. How much heat is removed from the gas.



So deltaU=0, Q=-W, So we have to know the area under the P-V curve, but how can we get the solution without calculus?
 
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We can't. Algebra-based textbooks just provide the appropriate equation and justify it by saying that it can obtained by using calculus.
 

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