Question

An Erlenmeyer flask of surface area 0.8 m2 and wall thickness 2 cm is filled with water at 0 oC. The Erlenmeyer flask is then immersed in a glass beaker filled with water at a temperature of 30 oC. What is the heat current? How long does it take for 12 J of heat energy to be transferred to the water in the Erlenmeyer flask?

Answer 1

Answer on Question#82064 - Physics - Molecular Physics - Thermodynamics

An Erlenmeyer flask of surface area $0.8\,\mathrm{m}^2$ and wall thickness $2\,\mathrm{cm}$ is filled with water at $0{}^{\circ}\mathrm{C}$. The Erlenmeyer flask is then immersed in a glass beaker filled with water at a temperature of $30{}^{\circ}\mathrm{C}$. What is the heat current? How long does it take for $12\,\mathrm{J}$ of heat energy to be transferred to the water in the Erlenmeyer flask?

Solution:

The heat conduction equation is given by

$$q = - \kappa \frac {\Delta T}{\Delta h},$$

Where $q$ – is the heat flux density $(\mathrm{W} \cdot \mathrm{m}^{-2})$, $\kappa$ – is the materials conductivity $(\mathrm{W} \cdot \mathrm{m}^{-1} \cdot \mathrm{K}^{-1})$, $\Delta T$ – is the temperature difference between wall faces (K) and $\Delta h$ – is the thickness of the wall (m).

Heat current is given by

$$J = q \cdot A,$$

Where $A$ – is the area of the surface.

Since $\Delta T = 30{}^{\circ}\mathrm{C} - 0{}^{\circ}\mathrm{C} = 30{}^{\circ}\mathrm{C}$, $\Delta h = 0.02\,\mathrm{m}$, $A = 0.8\,\mathrm{m}^2$ and the thermal conductivity of a common glass is $\kappa = 0.96\,\frac{\mathrm{W}}{\mathrm{m}\cdot\mathrm{K}}$, we obtain

$$J = - \kappa \frac {\Delta T}{\Delta h} A = - 0.96\,\frac{\mathrm{W}}{\mathrm{m}\cdot\mathrm{K}} \cdot \frac {30{}^{\circ}\mathrm{C}}{0.02\,\mathrm{m}} \cdot 0.8\,\mathrm{m}^2 = -1152\,\mathrm{W}$$

Since the heat current is defined as the energy loss during time $J = \Delta E / \Delta t$, we get the following

$$\Delta t = \frac {\Delta E}{J}$$

Since it is given that $\Delta E = -12\,\mathrm{J}$, we obtain

$$\Delta t = \frac {-12\,\mathrm{J}}{-1152\,\mathrm{W}} = 0.01\,\mathrm{s}$$

Answer: $J = -1152\,\mathrm{W}, \Delta t = 0.01\,\mathrm{s}$.

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