An ideal monatomic gas is taken through the cycle in the PV diagram below, in wh

Question

An ideal monatomic gas is taken through the cycle in the PV diagram below, in which each interval along the horizontal (V) axis is 6.00 L.

(Diagram: http://www.webassign.net/grr/p15-07alt.gif)

(a) If there are 0.0210 mol of this gas, what are the temperature and pressure at point C?
___ K
___ kPa
(b) What is the change in internal energy of the gas as it is taken from A to B?
___ J
(c) How much work is done by this gas per cycle?
___ J
(d) What is the total change in internal energy of this gas in one cycle?
___ J

Explanation / Answer

TA = pAVA/nR = 230x10^3*5000X10^-6/(0.015*8.314) = 9221K: TB = pBVB/nR = 98x10^3*5000X10^-6/(0.015*8.314) = 3929K dU = nCv*dT but Cv = 0.0150*12.47*(3929-9221) = -990J From A to B W= 0; From B - C W = p*(VC - VB) = 98x10^3*(10000x10^-6-5000x10^-6) = 490J From C to A = 1/2(pA + pC)*(VA - VC) = 1/2(230X10^3 + 98x10^3)*(5000x10^-6-10000x10^-6) = -820J So the total work = 490-820 = -330J

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