a 3.55 kg sample of an alloy is heated to 295 degree and plunged into an aluminium vessel containing 10.0L of water. the initial temperature of the vessel and water is 19 degree.the mass of the aluminium vessel is 2.1 kg and the specific heat of aluminium is 900 J kg-1K-1.
if the final temperature is 28.5 degree, find the specific heat of the alloy.
can anyone please help me with this question?tips?
thanks!
The heat lost by the alloy while cooling to the equilibrium temperature,
M' C' (295 - 28.5) = 3.55*266.5 C',
equals the heat gained by the water and vessel,
(Mw*Cw + M C)(28.5 - 19).
Write that statement as an algebraic equation and the only unknown will be the specific heat of the alloy, C'. Solve for it.
Mw and Cw are the mass and specific heat of water
M and C are the mass and specific heat of aluminum.
M' and C' are the mass and specific heat of the alloy. The only unknown is C'
thank you!
To find the specific heat of the alloy, we can set up an equation based on the principle of conservation of energy. The heat lost by the alloy while cooling is equal to the heat gained by the water and vessel.
First, let's calculate the heat lost by the alloy. The equation for heat transfer is Q = mcΔT, where Q is the heat transfer, m is the mass, c is the specific heat, and ΔT is the change in temperature.
For the alloy, the heat lost can be calculated as follows:
Q_alloy = m_alloy * c_alloy * ΔT_alloy
= (3.55 kg) * c_alloy * (295°C - 28.5°C)
Next, let's calculate the heat gained by the water and vessel. Similarly, the equation for heat transfer is used:
Q_water_vessel = (m_water + m_vessel) * c_water * ΔT_water_vessel
= (10.0 kg + 2.1 kg) * 900 J/(kg·K) * (28.5°C - 19°C)
According to the principle of conservation of energy, the heat lost by the alloy should be equal to the heat gained by the water and vessel, so we can set up the equation:
(m_water + m_vessel) * c_water * ΔT_water_vessel = (3.55 kg) * c_alloy * ΔT_alloy
Now, we can substitute the known values into the equation and solve for c_alloy:
(10.0 kg + 2.1 kg) * 900 J/(kg·K) * (28.5°C - 19°C) = (3.55 kg) * c_alloy * (295°C - 28.5°C)
From here, you can solve the equation for c_alloy to find the specific heat of the alloy.
I hope this explanation helps! Let me know if you have any further questions.