An alloy of mass 225g is heated to 550C. It is quickly placed in 450g of water at 12C. The water is contained in an aluminum calorimeter cup of mass 210g. The final temperature of mixture is 31.7C. Specific heat of aluminum is 0.215 cal/gC. Find the specific heat of alloy.
20 degree celcious
To find the specific heat of the alloy, we can use the principle of heat transfer, which states that the heat gained by the water is equal to the heat lost by the alloy and calorimeter.
Let's break down the problem step by step:
1. Calculate the heat gained by the water:
We can use the equation Q = mcΔT, where Q is the heat gained, m is the mass, c is the specific heat, and ΔT is the change in temperature.
The mass of the water, m_water, is given as 450g, the specific heat of water, c_water, is approximately 1 cal/gC, and the change in temperature, ΔT_water, is the final temperature (31.7C) minus the initial temperature (12C):
Q_water = m_water * c_water * ΔT_water
= 450g * 1 cal/gC * (31.7C - 12C)
2. Calculate the heat lost by the alloy and calorimeter:
The mass of the alloy, m_alloy, is given as 225g. We need to find the specific heat of the alloy, c_alloy. The mass of the calorimeter cup, m_cup, is given as 210g, and the specific heat of aluminum, c_cup, is given as 0.215 cal/gC. The change in temperature, ΔT_alloy_cup, is the final temperature (31.7C) minus the initial temperature (550C):
Q_alloy_cup = (m_alloy + m_cup) * c_cup * ΔT_alloy_cup
= (225g + 210g) * 0.215 cal/gC * (31.7C - 550C)
3. Apply the principle of heat transfer:
According to the principle of heat transfer, the heat gained by the water is equal to the heat lost by the alloy and calorimeter:
Q_water = Q_alloy_cup
So now we can set up the equation:
m_water * c_water * ΔT_water = (m_alloy + m_cup) * c_alloy * ΔT_alloy_cup
Plug in the known values:
450g * 1 cal/gC * (31.7C - 12C) = (225g + 210g) * c_alloy * (31.7C - 550C)
Simplify and solve for c_alloy:
c_alloy = (450g * 1 cal/gC * (31.7C - 12C)) / ((225g + 210g) * (31.7C - 550C))