Specific heat capacity of a certain metal is found by heating the metal and then placing it into water which is in a container made of the same material. The metal has mass of 100g and is heated to 100 degrees celsius. The container has mass of 200g and contains water of 500g of initially 20.0 degrees celsius. The final temperature of system is 21.4 degrees celcius. find the specific heat capacity of metal?
To find the specific heat capacity of the metal, we can use the principle of conservation of energy. The heat lost by the metal will be gained by the water and the container.
First, we need to calculate the heat gained by the water and the container. We can use the formula:
Qwater + Qcontainer = mcΔT
where Q is the heat gained, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
The mass of water is 500g, the mass of the container is 200g, and the change in temperature is the final temperature (21.4°C) minus the initial temperature of the water (20.0°C).
Qwater + Qcontainer = (500g)(4.18 J/g°C)(21.4°C - 20.0°C) + (200g)(c)(21.4°C - 20.0°C)
Qwater + Qcontainer = 2090 J + 200g(c)(1.4°C)
Now let's calculate the heat lost by the metal. We can use the formula:
Qmetal = mcΔT
where Q is the heat lost, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
The mass of the metal is 100g, and the change in temperature is the initial temperature (100°C) minus the final temperature of the system (21.4°C).
Qmetal = (100g)(c)(100°C - 21.4°C)
Qmetal = 7850g(c)
Since the heat lost by the metal is equal to the heat gained by the water and the container, we can set the two equations equal to each other:
Qmetal = Qwater + Qcontainer
7850g(c) = 2090 J + 200g(c)(1.4°C)
Now we can solve for c, the specific heat capacity of the metal.
7850g(c) = 2090 J + 280g(c)
7570g(c) = 2090 J
c = 2090 J / (7570g)
c ≈ 0.275 J/g°C
Therefore, the specific heat capacity of the metal is approximately 0.275 J/g°C.