A Glass Tea Kettle Containing 500 G of Water $0.090 \mathrm {~m} ^ { 2 }$

Multiple Choice

A glass tea kettle containing 500 g of water is on the stove. The portion of the tea kettle that is in contact with the heating element has an area of $0.090 \mathrm {~m} ^ { 2 }$ and is 1.5 mm thick. At a certain moment, the temperature of the water is $75 ^ { \circ } \mathrm { C }$ and it is rising at the rate of $3 \mathrm { C } ^ { \circ }$ per minute. What is the temperature of the outside surface of the bottom of the tea kettle? Neglect the heat capacity of the kettle, and assume that the inner surface of the kettle is at the same temperature as the water inside. The thermal conductivity of glass is $0.840 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$ and the specific heat of water is 4186 $\mathrm { J } / \mathrm { kq } \cdot \mathrm { K }$

A) $86 ^ { \circ } \mathrm { C }$
B) $77 ^ { \circ } \mathrm { C }$
C) $92 ^ { \circ } \mathrm { C }$
D) $120 ^ { \circ } \mathrm { C }$
E) $39 ^ { \circ } \mathrm { C }$