A gas is isochorically heated from 300 K to 400 K. The initial pressure is 0.1 MPa. If you wanted to calculate the final pressure, which of the following equations is the most simplified and correct?
A.?P=?_(400 K)^(300 K)?(?P/?T)_?V dT+?_(?V_1)^(?V_2)?(?P/(??V))_T d?V
B.?P=?_(400 K)^(300 K)?(?P/?T)_?V dT+?_(P_1)^(P_2)?(?P/(??V))_T dP
C.?P=?_(300 K)^(400 K)?(?P/?T)_?V dT
D.P-0.1 MPa=?_(300 K)^(400 K)??(?P/?T)_?V dT?+?_(?V_1)^(?V_2)?(?P/?T)_?V d?V
E.None of these are correct.
A. Incorrect. Your limits are incorrect in the first term and the second term can be simplified.
B. Incorrect. The second term is not derived correctly. Restart from Equation 6.2.
C. Correct. The second term in the total derivative (molar volume) disappears because the heating is isochoric. Now we need an equation of state to process the partial derivative.
D. Incorrect. The right hand side can be simplified further.
E. Incorrect. One of these equations is a correct total derivative for this situation.
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