To calculate the time taken to raise the temperature of an aluminum block from 28°C to 108°C using a 1000W heat source, we can apply the formula:
Q = mcΔT
where: Q is the heat energy transferred m is the mass of the aluminum block c is the specific heat capacity of aluminum ΔT is the change in temperature
First, let's find the heat energy required to raise the temperature of the aluminum block:
Q = mcΔT
m = 700g = 0.7 kg (converting grams to kilograms) c = 0.897 J/g°C (specific heat capacity of aluminum) ΔT = (108°C - 28°C) = 80°C
Q = (0.7 kg) * (0.897 J/g°C) * (80°C) Q = 50.4 kJ (kilojoules)
Next, we can calculate the time required using the power formula:
Power (P) = Energy (Q) / Time (t)
Given: P = 1000W (power of the heat source) Q = 50.4 kJ = 50400 J (converting kilojoules to joules)
t = Q / P t = 50400 J / 1000W t = 50.4 seconds
Therefore, it would take approximately 50.4 seconds to raise the temperature of the 700g aluminum block from 28°C to 108°C using a 1000W heat source.