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Unformatted text preview: 12-4CYes.12-8It is to be proven for an ideal gas that the P= constant lines on a T-vdiagram are straight lines and that the high pressure lines are steeper than the low-pressure lines.Analysis(a) For an ideal gas Pv= RTor T= Pv/R. Taking the partial derivative of Twith respect to v holding Pconstant yieldsRPTP=∂∂vwhich remains constant at P= constant. Thus the derivative (∂T/∂v)P, which represents the slope of the P= const. lines on a T-vdiagram, remains constant. That is, the P= const. lines are straight lines on a T-vdiagram.(b) The slope of the P= const. lines on a T-vdiagram is equal to P/R, which is proportional to P. Therefore, the high pressure lines are steeper than low pressure lines on the T-v diagram.12-10Nitrogen gas at a specified state is considered. The cpand cvof the nitrogen are to be determined using Table A-18, and to be compared to the values listed in Table A-2b....
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- Spring '08
- Derivative, T-v diagram, high pressure lines