Water is boiled in a container whose bottom has a surface area of 25 cm^2 , a thickness of 1.0 mm , and a thermal conductivity of 50 W m^ -1 ^ ^ ^ ^ -1 . After boiling begins, 100 g of water is converted into steam per

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Quantrex Academy · Accepted Answer

Correct answer: C. 130 ^ ^ ^ C

The rate of heat transfer through the bottom of the container is given by Fourier's law of heat conduction:

\dfrac{dQ}{dt} = \dfrac{KA(T_2 - T_1)}{d}

The rate of heat utilized in boiling the water is:

\dfrac{dQ}{dt} = \dfrac{mL}{t}

Equating the two rates of heat transfer:

\dfrac{KA(T_2 - T_1)}{d} = \dfrac{mL}{t}

Substituting the given values,

K = 50 \text{ W m}^{-1} ^{{}^{{}^{\circ}}}\textC^{-1}

,

A = 25 \times 10^{-4} \text{ m}^2

,

d = 10^{-3} \text{ m}

,

m = 0.1 \text{ kg}

,

t = 60 \text{ s}

,

L = 2.26 \times 10^6 \text{ J kg}^{-1}

, and

T_1 = 100 ^{{}^{{}^{\circ}}}\text{C}

:

\dfrac{50 \times 25 \times 10^{-4} \times (T_2 - 100)}{10^{-3}} = \dfrac{0.1 \times 2.26 \times 10^6}{60}

125(T_2 - 100) = \dfrac{226000}{60}

125(T_2 - 100) = \dfrac{11300}{3}

T_2 - 100 = \dfrac{11300}{375} \approx 30.13 ^{{}^{{}^{\circ}}}\text{C}

T_2 = 100 + 30.13 = 130.13 ^{{}^{{}^{\circ}}}\text{C}

The temperature of the lower surface is approximately

130 ^{{}^{{}^{\circ}}}\text{C}

.

Water is boiled in a container whose bottom has a surface area of...

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