Answer:
The rate of conductive heat transfer Q/t is approximately 3.158 Watts
Explanation:
The given parameters of the Styrofoam cup are;
The thermal conductivity of the cup, k = 0.010 W/(m·°C)
The cross-sectional area of the cup, A = 3.0 × 10⁻² m²
The thickness of the cup, L = 0.589 cm = 0.00589 m
The temperature of the coffee (in the cup) = 89°C, T₂ = 86.0 °C
The temperature of the air in the room (of the cup of coffee), T₁ = 24.0°C
The rate of conductive heat transfer of the cup of coffee, Q/t, is given by the following formula;
![\dfrac{Q}{t} = \dfrac{k \cdot A \cdot (T_2 - T_1)}{L}](https://tex.z-dn.net/?f=%5Cdfrac%7BQ%7D%7Bt%7D%20%3D%20%5Cdfrac%7Bk%20%5Ccdot%20A%20%5Ccdot%20%28T_2%20-%20T_1%29%7D%7BL%7D)
Plugging in the value of the variables, in the above equation, gives;
![\dfrac{Q}{t} = \dfrac{0.010 \, W/(m\cdot ^{\circ }C) \times 3.0 \times 10^{-2} m^2 \times (86.0 ^{\circ} C - 24.0^{\circ}C)}{0.00589 \, m} = \dfrac{60}{19} \ W](https://tex.z-dn.net/?f=%5Cdfrac%7BQ%7D%7Bt%7D%20%3D%20%5Cdfrac%7B0.010%20%5C%2C%20W%2F%28m%5Ccdot%20%5E%7B%5Ccirc%20%7DC%29%20%5Ctimes%203.0%20%5Ctimes%2010%5E%7B-2%7D%20m%5E2%20%5Ctimes%20%2886.0%20%5E%7B%5Ccirc%7D%20C%20-%2024.0%5E%7B%5Ccirc%7DC%29%7D%7B0.00589%20%5C%2C%20m%7D%20%3D%20%5Cdfrac%7B60%7D%7B19%7D%20%5C%20W)
The rate of conductive heat transfer of the cup of coffee, Q/t = 60/19 W =
W ≈ 3.158 W.