1.5 kg of an unknown liquid at a temperature of 17 degrees Celsius is added to 2kg of water at 50C. The final temp of the mixture is 45C. Assuming no heat is lost to the environment, determine the specific heat capacity of the unknown liquid.
So I assume you would do
Qmct = qmct
And then solve for the q of the unknown and then plug the q into the specific latent formula and solve for the lf? I don't think that's right though, I'm not sure. I would really appreciate the help!
heat lost by water = heat gained by unknown
your method is fine
To determine the specific heat capacity of the unknown liquid, we can use the principle of conservation of energy. The heat lost by the hot water is equal to the heat gained by the cool unknown liquid.
First, let's calculate the heat lost by the water using the formula Q = mcΔt, where Q is the heat lost, m is the mass, c is the specific heat capacity, and Δt is the change in temperature.
Q_water = m_water * c_water * Δt_water
Q_water = 2kg * c_water * (50°C - 45°C)
Q_water = 10kg°C * c_water
Now, let's calculate the heat gained by the unknown liquid using the same formula.
Q_unknown = m_unknown * c_unknown * Δt_unknown
Q_unknown = 1.5kg * c_unknown * (45°C - 17°C)
Q_unknown = 28.5kg°C * c_unknown
Since we assume no heat is lost to the environment, the heat lost by the water is equal to the heat gained by the unknown liquid.
Q_water = Q_unknown
10kg°C * c_water = 28.5kg°C * c_unknown
Now we can solve for c_unknown:
c_unknown = (10kg°C * c_water) / (28.5kg°C)
So, to find the specific heat capacity of the unknown liquid, you would divide the specific heat capacity of water by 28.5 kg°C and then multiply it by 10 kg°C.
Please note that the specific heat capacity of water is approximately 4.18 J/g°C. So if you convert your answer from joules to grams, it will give you the specific heat capacity in J/g°C.