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Hint: Rate of heat flow derived from the temperature gradient relates thermal conductivity with temperature difference and heat lost at time. Substitute the values in $H = \dfrac{{\Delta Q}}{t} = KA\dfrac{{dT}}{l}$ to find heat lost for time t. From the latent heat formula calculate the mass of ice reduced for heat Q in one minute.
Complete step-by-step solution
The heat is getting transferred by conduction.
The rate of flow of heat is given by,
$H = \dfrac{{\Delta Q}}{t} = KA\dfrac{{dT}}{l}$
Here; K is conductivity; A is the area of the cross section; t is the time; dT is the difference in temperature and I is the length of the conductor.
Given:
\[
K = 30W/m{\text{ }}K \\
L = 80cal/gm \\
A = 5c{m^2} \\
l = 25cm \\
dT{\text{ }} = {100^0}C \\
t = 60s. \\
\]
Substitute in the expression
$
\Delta Q = \dfrac{{30 \times 5 \times {{10}^{ - 4}} \times 60 \times 100}}{{25 \times {{10}^{ - 2}}}} \\
\Delta Q = 6J/s \\
$
We know that heat required to melt ice=\[Q = mL\] , where, \[m\] is the mass of ice.
$
m = \dfrac{{360}}{{80 \times 4.2}} \\
m = 1.07gm \\
$
Hence the mass of ice melted in one minute is 1.07 gm and the correct option is B.
Note: Thermal resistance of a body is a measure of its opposition to the flow of heat through it. It is defined as the ratio of temperature difference to the heat current. It is denoted by R . Its unit is \[Ks/kcal.\]
$R = \dfrac{{dT}}{H} = \dfrac{l}{{KA}}$ .
If it is difficult to remember the heat flow equation, then just recall the formula from electrodynamics
$R = \dfrac{V}{i}$; And $R = \dfrac{l}{{kA}}$ here V is the voltage (analogous to temperature difference), i is the current (analogous to rate of heat transfer), k is the conductivity (similar to the heat conductivity in the question).
Complete step-by-step solution
The heat is getting transferred by conduction.
The rate of flow of heat is given by,
$H = \dfrac{{\Delta Q}}{t} = KA\dfrac{{dT}}{l}$
Here; K is conductivity; A is the area of the cross section; t is the time; dT is the difference in temperature and I is the length of the conductor.
Given:
\[
K = 30W/m{\text{ }}K \\
L = 80cal/gm \\
A = 5c{m^2} \\
l = 25cm \\
dT{\text{ }} = {100^0}C \\
t = 60s. \\
\]
Substitute in the expression
$
\Delta Q = \dfrac{{30 \times 5 \times {{10}^{ - 4}} \times 60 \times 100}}{{25 \times {{10}^{ - 2}}}} \\
\Delta Q = 6J/s \\
$
We know that heat required to melt ice=\[Q = mL\] , where, \[m\] is the mass of ice.
$
m = \dfrac{{360}}{{80 \times 4.2}} \\
m = 1.07gm \\
$
Hence the mass of ice melted in one minute is 1.07 gm and the correct option is B.
Note: Thermal resistance of a body is a measure of its opposition to the flow of heat through it. It is defined as the ratio of temperature difference to the heat current. It is denoted by R . Its unit is \[Ks/kcal.\]
$R = \dfrac{{dT}}{H} = \dfrac{l}{{KA}}$ .
If it is difficult to remember the heat flow equation, then just recall the formula from electrodynamics
$R = \dfrac{V}{i}$; And $R = \dfrac{l}{{kA}}$ here V is the voltage (analogous to temperature difference), i is the current (analogous to rate of heat transfer), k is the conductivity (similar to the heat conductivity in the question).
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