Question:

A 2kg metal block is initially at a temperature of 25°C. The block is heated until its temperature reaches 175°C. During this process, 2500 J of heat energy is added to the block.

a) Calculate the specific heat capacity of the metal.

b) Determine the change in internal energy of the metal block.

c) Calculate the amount of heat transfer if the metal block is cooled back to its initial temperature of 25°C.

Given specific heat capacity of the metal = 0.5 J/g°C.

Answer:

a) The formula to calculate the heat energy transferred to an object is given by:

q = mcΔT

Where: q = heat energy transferred (in joules) m = mass of the object (in kg) c = specific heat capacity of the material (in J/g°C or J/kg°C) ΔT = change in temperature (in °C)

To calculate the specific heat capacity of the metal, we rearrange the formula as follows:

c = q / (m * ΔT)

Given: m = 2 kg ΔT = (175°C - 25°C) = 150°C q = 2500 J

Substituting these values into the formula, we get:

c = 2500 J / (2 kg * 150°C)

c = 8.33 J/kg°C

Therefore, the specific heat capacity of the metal is 8.33 J/kg°C.

b) The change in internal energy of the metal block can be calculated using the formula:

ΔU = mcΔT

Where: ΔU = change in internal energy (in joules) m = mass of the object (in kg) c = specific heat capacity of the material (in J/g°C or J/kg°C) ΔT = change in temperature (in °C)

Given: m = 2 kg ΔT = (175°C - 25°C) = 150°C c = 8.33 J/kg°C (as calculated in part a)

Substituting these values into the formula, we get:

ΔU = 2 kg * 8.33 J/kg°C * 150°C

ΔU = 2499 J

Therefore, the change in internal energy of the metal block is 2499 J.

c) The amount of heat transfer when the metal block is cooled back to its initial temperature can be calculated using the formula:

q = mcΔT

Given: m = 2 kg ΔT = (175°C - 25°C) = 150°C c = 8.33 J/kg°C (as calculated in part a)

Substituting these values into the formula, we get:

q = 2 kg * 8.33 J/kg°C * (-150°C)

q = -2499 J

Therefore, the amount of heat transfer when the metal block is cooled back to its initial temperature is -2499 J (negative sign indicates heat transfer out of the block).

Note: The negative sign indicates that the heat energy is being transferred out of the block as it is being cooled back.