ch19-p082 - 82 To model the uniform rates described in the...

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82. To model the “uniform rates” described in the problem statement, we have expressed the volume and the temperature functions as follows: V = V i + © ¨ § ¹ ¸ · V f V i τ f t and T = T i + © ¨ § ¹ ¸ · T f T i τ f t where V i = 0.616 m 3 , V f = 0.308 m 3 , τ f = 7200 s, T i = 300 K and T f = 723 K. (a) We can take the derivative of V with respect to t and use that to evaluate the cumulative work done (from t = 0 until t = ): W = ´ p dV = ´ © ¨ § ¹ ¸ · nRT V © ¨ § ¹ ¸ · dV dt dt = 12.2 + 238113 ln(14400 ) 2.28 × 10 6 with SI units understood. With = f our result is W = 77169 J ≈− 77.2 kJ, or | W | 77.2 kJ. The graph of cumulative work is shown below. The graph for work done is purely negative because the gas is being compressed (work is being done on the gas). (b) With C V = 3 2 R (since it’s a monatomic ideal gas) then the (infinitesimal) change in internal energy is nC V dT = 3 2 nR © ¨ § ¹ ¸ ·
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ch19-p082 - 82 To model the uniform rates described in the...

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