When a 2Kg block of metal at 600°C is put into water at its boiling point, 0.5 kg of steam is released. Find the specific heat capacity of the metal?
To find the specific heat capacity of the metal, we can use the principle of conservation of energy. We can calculate the heat gained by the water and then equate it to the heat lost by the metal.
First, let's calculate the heat gained by the water using the formula:
Q = m * L
where Q is the heat gained, m is the mass of the water, and L is the latent heat of vaporization of water.
Given that 0.5 kg of steam is released, the mass of the water is also 0.5 kg.
The latent heat of vaporization of water is 2260 kJ/kg.
So, the heat gained by the water is:
Q = 0.5 kg * 2260 kJ/kg
= 1130 kJ
Now, let's calculate the heat lost by the metal.
The formula to calculate heat transfer is:
Q = m * C * ΔT
where Q is the heat lost, m is the mass of the metal, C is the specific heat capacity of the metal, and ΔT is the change in temperature.
The mass of the metal is 2 kg.
The change in temperature is the difference between the initial temperature of the metal and the boiling point of water, which is 100 °C.
So, the heat lost by the metal is:
Q = 2 kg * C * (600 °C - 100 °C)
= 1000 kg * C °C
Now, according to the principle of conservation of energy:
Heat gained by water = Heat lost by metal
Therefore,
1130 kJ = 2 kg * C °C
Simplifying the equation:
C = 1130 kJ / 2 kg
= 565 kJ/kg
So, the specific heat capacity of the metal is 565 kJ/kg.