Question:

A 2 kg piece of iron is heated from 20°C to 80°C. The specific heat capacity of iron is 449 J/kg°C.

a) Calculate the amount of heat energy required to raise the temperature of the iron piece.

b) If the same amount of heat energy is supplied to 4 kg of water at an initial temperature of 25°C, what will be the final temperature of the water? The specific heat capacity of water is 4186 J/kg°C.

Answer:

a) The amount of heat energy (Q) required to raise the temperature of an object can be calculated using the following formula:

Q = m * c * ΔT,

where Q is the heat energy, m is the mass of the object, c is the specific heat capacity, and ΔT is the change in temperature.

Given: Mass of iron (m) = 2 kg Specific heat capacity of iron (c) = 449 J/kg°C Change in temperature of iron (ΔT) = (80°C - 20°C) = 60°C

Plugging in the values:

Q = 2 kg * 449 J/kg°C * 60°C = 53880 J = 53.88 kJ

Therefore, the amount of heat energy required to raise the temperature of the iron piece is 53.88 kJ.

b) To find the final temperature of the water, we can rearrange the formula Q = m * c * ΔT to solve for ΔT:

ΔT = Q / (m * c)

Given: Mass of water (m) = 4 kg Specific heat capacity of water (c) = 4186 J/kg°C Heat energy supplied to water (Q) = 53.88 kJ = 53880 J

Plugging in the values:

ΔT = 53880 J / (4 kg * 4186 J/kg°C) ≈ 3.23°C

Since the initial temperature of the water is 25°C, the final temperature can be calculated as:

Final temperature = Initial temperature + ΔT = 25°C + 3.23°C ≈ 28.23°C

Therefore, the final temperature of the water will be approximately 28.23°C.