Question

The ideal gas law gives the following formula governing the number of moles of a gas in terms of temperature, pressure, and volume: PV n(T, V, P) = 8.31 . T (a) Find the differential dn of n(T, V, P). (b) You use the ideal gas law to count the number of moles of helium gas in a chamber by measuring pressure, volume and temperature (because, you know, gas is invisible). You make measurements, with the following known possible errors coming from the precision of your instruments: V 110-6)m3,P (10° 3)Pa, and T-(250+0.1) K. Use the differential dn found in the previous item to estimate the maximal error in your measurement of the number of moles

Answer 1

n = PV/8.31T = 48.135moles taking log both sides implies log n = log(PV) -log(8.31T) implies log n = log P + log v -log 8.31 -log T Taking differential both sides implies delta n/n = delta P/P + delta V/V + delta T/T implies delta n = n(delta P/P + delta V/V + delta T/T) or dn = n(dp/p + dv/v + dT/T) (b) V = (1 plusminus 10^-6)m^3 P = (10^5 plusminus 3)pa T = (250 plusminus 0.1)k implies dn = 0.021moles so n = (48.135 plusminus 0.021)moles

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