An insulated copper block that receives energy at a rate of 100 W from an embedded resistor, as shown in the figure below. If the block has a volume of 0.001 m? and an initial temperature of 20&d

To solve this problem, we need to use the formula Q = mc?T, where Q is the amount of heat transferred, m is the mass of the block, c is the specific heat capacity of copper, and ?T is the change in temperature. First, we can calculate the mass of the block using the density of copper, which is 8,960 kg/m?: mass = density x volume mass = 8,960 kg/m? x 0.001 m? mass = 8.96 kg Next, we need to find the amount of heat transferred to the block: Q = P x t Q = 100 W x t We don't know the time t, but we can find it by setting the amount of heat transferred equal to the amount of heat needed to raise the temperature of the block from 20°C to 60°C: Q = mc?T Q = 8.96 kg x 385 J/kg°C x (60°C - 20°C) Q = 10,312.96 J Setting these two equations equal to each other and solving for t: 100 W x t = 10,312.96 J t = 103.13 seconds or 1.72 minutes (rounded to two decimal places) Therefore, it would take \approx imately 1.72 minutes for the temperature of the copper block to reach 60°C.