Question

An ice cube at 0c measures 10 cm of a side. It sits on top of a copper block with square cross section 10 cm 10 cm and length of 20 cm. The other end of the block of copper is in contact with large pool of water kept at 90c. Conductivity of copper is 400 w/mk and density of ice is 0.9 gm/cc. In what time (in sec) is ice completely melted? Assume that ice cube melts only from surface in contact with copper. (j = 4.2 j/cal)

Answer 1

Given:

Temperature of ice cube = 0°C

Edge of the ice cube = 10 cm

Length of the copper block = 20 cm

Width and height of the copper block = 10 cm =0.01 m

conductivity of copper, k = 400 W/m·K

Density of ice, $\rho =0.9 gm/cc$

Latent heat of fusion of ice, $L_f=334 J/g$

Calculations:

Mass of ice

$m =\rho V\\V = (10cm)^3 =10^3 cc\\m= 0.9\times 10^3 \\m= 900 g$

$Q_1=mL_f\\Q_1=900g\times 334 J/g \\Q_i= 3.01\times 10^5J$

$\frac{Q_c}{t}=\frac{kA\Delta T}{l}\\\frac{Q_c}{t}=\frac{400 W/mK\times 0.1^2m^2\times 90 K}{0.20m}=1800 J/s$

$t=Q_i/Q_c\\t = \frac{3.01\times 10^5}{1800} = 167.22 s = 2.78 min$

Learn more about: Modes of Heat transfer

brainly.in/question/1749498

#learnwithbrainly