A piece of metal is 5.0m long and has a cross-sectional area of 0.2m^2 . One end

Question

A piece of metal is 5.0m long and has a cross-sectional area of 0.2m^2
.
One end of this metal is in contact with a water-steam mixture at 100C,
and the other end is in contact with a water-ice mixture at 0C. The latent
heat of vaporization is 2.2×10^6 J
kg , and the latent heat of fusion is 3.3×10^5 Jkg

.
(a). If 1.5 × 10^4kg of steam condense every second, what is the thermal
conductivity k of the metal?
(a) 17 W
(b) ** 83
(c) 330 W
(d) 410 W
(e) 2100 W
m K
(b). If the length of the piece of metal and its cross-sectional area were
both doubled the rate of energy transfer would:
(a) increase by a factor of 4.
(b) increase by a factor of 2.
(c) ** stay the same.
(d) decrease by a factor of 2.
(e) decrease by a factor of 4

Explanation / Answer

a) 83 Wmk

A = 0.2 m^2

dT = (100 - 0)

= 100 C

L = 0.5 m

rate of heat transfered, dQ/dt = m*Lv

= 1.5*10^-4*2.2*10^6

= 330 W

rate of heat transfred, dQ/dt = k*A*dT/L

k = (dQ/dt)*L/(A*dT)

= 330*5/(0.2*100)

= 82.5 Wmk (appoximately 83 Wmk)

2) (c) stay the same.

because, (dQ/dt)' = k*A'*dT/(L')

= k*2A*dT/(2*L)

= k*A*dT/L

= dQ/dt

rate of heat tranfered does not change.

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