If the heat capacity of a substance is correctly represented by an equation of t
ID: 503679 • Letter: I
Question
If the heat capacity of a substance is correctly represented by an equation of the form, Cp = A + BT + CT^2 show that the error resulting when <Cp>h is assumed to equal Cp evaluated at the arithmetic mean of the initial and final temperatures is C(T2-T1)^2/12 s, irthe heat capacity ofasubstanceis correctly represented by an equation of the form, cr A+ BT +CT show that the emor resulting when (CP)H is assumed equal to Cr evaluated at the arithmetic mean ofthe initial and final temperatures is COT, -T /12.Explanation / Answer
Cp=A+BT+CT2
Cpave=A+B*(T2+T1)/2 +C*{(T2+T1)/2}2,
<CP>H=
= { A*(T2-T1) + B*(T22-T12)/2 +C(T23-T13)/3}/(T2-T1)
=A + B*(T2+T1)/2 +C*(T22+T12+T2T1)/3
<CP>H- Cpave= C*(T22+T12+T2T1)/3- C*(T22+T12+2T1T2)/4
=C*( 4T22+4T12+4T1T2-3T22-3T12-6T1T2)/12
=C*(T22+T12-2T1T2)/12= C*(T2-T1)2/12