ME_302_Optional_Bonus_Homework

# ME_302_Optional_Bonus_Homework - ME 302 Optional Bonus...

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ME 302 Optional Bonus Homework 1) One simple correction for the ideal gas law to increase its accuracy at high pressures is to add a co-volume, b : ±² ³ ´µ ¶ ·¸ a. Calculate the compressibility factor, Z , for this equation of state. b. For a general equation of state ¹º ¶ »²¼¹¸ ½¼¾¸ ¿ À ÁÂ ÁÃ ÄÅ Æ ³ ÇÈ ¹² , calculate du for the above equation of state. c. For a general equation of state ¹É ¶ »Ç¼¹¸ ½¼Ê²³¸ ¿ À ÁÆ ÁÃ ÄÅ Â Ë ¹Ç , calculate dh for the above equation of state. d. For a general equation of state: »Ç ³ »² ¶ ¸² Ì Í Î Ï Í , where Ð Ã Ñ Ò Æ ¿ À ÁÆ ÁÃ ÄÅ Â is the coefficient of thermal expansion and Ó Ã Ñ ³ Ò Æ ¿ À ÁÆ ÁÂ ÄÅ Ã is the isothermal compressibility. Calculate »Ç ³ »² for the above equation of state. e. Starting from both of the general Tds relations, derive both equations to calculate the change of entropy for a fluid obeying the above equation of state assuming constant specific heats. f. Derive the temperature, pressure, and specific volume relations (you should get three equations involving the specific heat ratio) for an isentropic process for the above equation of state. g. Calculate the boundary work per unit mass, Ô ÒÕ , for an isentropic process. 2) A pyrometer is a device that is used to measure the surface temperature of an object using thermal radiation. The common infrared thermometer is a simple example of a pyrometer. A schematic of a one-color pyrometer is shown below. Radiation emitted by an object is collected

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## This note was uploaded on 10/04/2011 for the course ME 302 taught by Professor Helum during the Spring '11 term at Penn State.

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ME_302_Optional_Bonus_Homework - ME 302 Optional Bonus...

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