InterviewSolution
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InterviewSolution
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Find the minimum attainable pressure of ideal gas in the process `T = T_0 + alpha V^2`, where `T_0` and `alpha` positive constants, and `V` is the volume of one mole of gas. Draw the approximate `p vs V` plot of this process. |
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Answer» `T = T_0 + alpha V^2 = T_0 + alpha (R^2 T^2)/(p^2)` (as, `V = RT//p-` for one mole of gas) So, `p = sqrt(alpha) RT (T - T_0)^(1//2)` ….(1) For `P_(min), (dp)/(dT) = 0`, which gives `T = 2 T_0` …(2) From (1) and (2), we get, `p_(min) = sqrt(alpha) R 2 T_0 (2 T_0 - T_0)^(-1//2) = 2 R sqrt(alpha T_0)`. |
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