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Thermodynamics

# A steel rod of length 20 cm and cross sectional area 3 $cm^{2}$ is heated at one end to $\;300^{0}C\;$ and the other end is in ice . Assuming no loss of heat , the mass of ice that melts in 10 minutes if $\;K_{steel} = 0.16 \;C.G.S\;$ units .

$(a)\;54\;grams\qquad(b)\;27\;grams\qquad(c)\;108\;grams\qquad(d)\;270\;grams$

Answer : $\;54\;grams$
Explanation :
Rate of heat flow = $\large\frac{KA (T_{1}-T_{2})}{L}$
$= \large\frac{0.16 \times 3 (300)}{20}$
$= 7.2 \;C.G.S.$ units
Heat transferred in 10 minutes
$=72 \times 10 \times 60$
$Q = 72 \times 60$
Let mass of ice melted be m
$Q = mL$
$72 \times 60 = m\times 80$
$m = 54 \;grams$