Question

Consider two houses that are identical except that the walls are built using bricks in one house and wood in the other. If the walls of the brick house are twice as thick, which house do you think will be more energy efficient?

Short answer

Answer: The wood house is more energy efficient due to its lower heat transfer rate compared to the brick house.

Step-by-step solution

Define heat transfer rate equation

We will use the heat transfer equation to calculate the rate at which heat is transferred through the walls of both houses. The heat transfer rate through a surface is given by: Q = U * A * ∆T Where Q is the heat transfer rate, U is the overall heat transfer coefficient, A is the surface area in contact, and ∆T is the temperature difference across the surface. We need to find the heat transfer coefficient (U) for both brick and wood to compare their energy efficiency.

Calculate heat transfer coefficients for brick and wood

We will use the thermal conductivity (k) values of brick and wood to find the heat transfer coefficients for both materials. Thermal conductivity of brick: k_b = 0.6 W/(m*K) Thermal conductivity of wood: k_w = 0.15 W/(m*K) Thickness of brick wall: d_b = 2*d_w (since the brick wall is twice as thick) Thickness of wood wall: d_w The heat transfer coefficient U is determined by: U = k / d For brick: U_b = k_b / d_b For wood: U_w = k_w / d_w However, since we don't have the values of both thicknesses, we can analyze the ratio of heat transfer coefficients to determine the relative energy efficiency of both houses.

Compare the heat transfer coefficients

By analyzing the ratio of heat transfer coefficients, we can determine which house is more energy efficient. U_b / U_w = (k_b / d_b) / (k_w / d_w) Substituting d_b = 2*d_w U_b / U_w = (k_b / (2*d_w)) / (k_w / d_w) U_b / U_w = (0.6 / (2*d_w)) / (0.15 / d_w) After simplification, we find: U_b / U_w = 2

Determine the more energy efficient house

Since the ratio of U_b to U_w is 2, this means that the heat transfer rate in the brick house is twice as high as that in the wood house. Thus, the wood house has a lower heat transfer rate, making it more energy efficient. In conclusion, the wood house will be more energy efficient due to its lower heat transfer rate compared to the brick house.