A nickel wire 2 1mm in cross-sectional area and 100cm long is stretched uniforml
ID: 2075772 • Letter: A
Question
A nickel wire 2 1mm in cross-sectional area and 100cm long is stretched uniformly in tension–elastically, isothermally, and reversibly- at 300K from its rest position to a stress of 5 2 10 dyn cm and then cut.
a) Calculate the work being performed, the heat flow into the wire, and the wire’s change in internal energy during the stressing process.
b) When the wire is cut, what is its change in temperature?
c) What is the entropy change of the universe associated with this irreversible process? Hint: You will need some extra information, such as density, specific heat, coefficient of linear expansion of Nickel. You may ignore the temperature dependence for Young modules of Nickel
Explanation / Answer
length of the wire = 100 cm
dia = 21 mm
area = 3.14*(10.5*e-3)2 = 3.46e-4 sq.m
stress = 52e+10 dyn-cm
volume of the wire = 100*3.46 = 346 cc
stress = 52e+10 /346 = 1.50 e+9 dyn/sq.cm
= 1.5e+8 N/sq.m
Y- of Nickel = stress/strain = 170e+9 N/m2
strain in the wire
dL/L = 1.5e+8 /170e+9
L = 100cm
elongation of the wire dL = (1.5e+8/170e+9)*100 = 0.09 cm
Force = 1,5e+8 * 3.46e-4 = 5.19e+4 N
work done = F*ds = 5.19e+4 *0.09e-2 = 46.71 J
It is an isothermal process and no chnage in temp.
=> no change in internal energy
The wire is stretched elastically => no heat flow into the wire
b) when the wire is cut, the pressure is released, it is reversible process
work done 46.71 J is supplied to the wire as heat
specific heat of Nickel 0.44 kJ/kg-K
density of Nickel =8908 kg/m3
mass of the wire = 8908*346e-6 = 3.08e-2 kg
raise in temp of the wire (T) : 0.44e+3*3.08e-2*T = 46.71 J
T = 3.45 C deg.
entropy change = dQ/T = 46.71/300 = 0.1557 J/K
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