The correct answer is in Red. The specific volume of air can be determined by me

Question

The correct answer is in Red.

The specific volume of air can be determined by measuring its pressure and temperature for insertion in the ideal gas equation of state (Pv = RT). For a particular experiment, temperature is measured as 25 plusminus 0.5 degree C and pressure is measured to be 101.325 plusminus 0.5 kPa. The value of R for air is 287 J.kg^-1 K^-1 and may be assumed to be exact. For the above conditions, the overall random error associated with the calculated air specific volume is given by: plusminus 0.00248 m^3 middot kg^-1 plusminus 0.0044 m^3 middot kg_1 plusminus 0.00531 m^3 middot kg^-1 plusminus 0.00813 m^3 middot kg^-1

Explanation / Answer

Fractional error in pressure (dP/P) =( 0.5/101.325 )= 0.0049346

Fractional error in Temperature(dT/T) = (0.5/(273+25)) = 0.0016778

Resultant error fraction in specific volume is sqrt ( (dP/P)2 + (dT/T)2) = sqrt ( 0.0049346^2 + 0.0016778^2) = 0.005212033193.

Specific volume = RT/P = 287 *(25+273) /101325 = 0.84407599m3/kg

Error = 0.005212033193*0.84407599 = 0.004399 m3/kg

Refer page "http://lectureonline.cl.msu.edu/~mmp/labs/error/e2.htm" for quick understanding of error analysis.

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