A 50W electric heater is used to heat a metal block of mass 5kg. If in 10 minutes a temperature rise of 12oC is achieved, the specific heat capacity of the ...

A 50W electric heater is used to heat a metal block of mass 5kg. If in 10 minutes a temperature rise of 12oC is achieved, the specific heat capacity of the metal is

Answer Details

The specific heat capacity of a substance is the amount of energy required to raise the temperature of 1 kilogram of that substance by 1 degree Celsius. In this problem, we have a 50W electric heater that is used to heat a metal block of mass 5kg. We are also given that the temperature of the block increases by 12°C in 10 minutes. To find the specific heat capacity of the metal, we can use the formula: Q = mcΔT where Q is the amount of heat energy transferred, m is the mass of the metal block, c is the specific heat capacity of the metal, and ΔT is the change in temperature of the metal block. We know that the electric heater is supplying 50J of heat energy per second (since 1W = 1J/s), and the heater is operating for 10 minutes, or 600 seconds. Therefore, the total amount of heat energy supplied to the metal block is: Q = (50 J/s) x (600 s) = 30,000 J We also know that the mass of the metal block is 5kg, and the temperature of the block increases by 12°C. Therefore, we can rearrange the formula above to solve for the specific heat capacity: c = Q/(mΔT) = 30,000 J/(5 kg x 12°C) = 500 J/(kg·°C) Therefore, the specific heat capacity of the metal is 500 J/(kg·°C). So, the correct option is: 500 J kg-1K-1.