3) You pour 240 mL of Coke into a glass, where the T of the beverage is at 10.5 *C. You then add one ice cube of 45g.
Determine the final temperature and the amount of ice remaining, if any.
So I know that there won't be any more ice left because they will reach thermal equilibrium, and the temperature will be over 0*C.
q for ice will be
= (4.184 J/gK)(45g)(Tf-Ti)
But I have no idea how to go about deltaT and what to do next.
Thank you
You need to rething this. You will have ice left over.
45g x 334 J/g = 15030 J available.
To cool the water to 0 C we need
240 x 4.184 x (10.5) = 10,540.7 SO WE have more cooling than we need. Some ice will be left over after cooling to zero C. I figured we need melt only 31.5 g but you need to confirm that. I estimatredf here and there and I'm not positive about the 334 value I used above.
solve q initial for the 240g of coke/water.
solve q initial for the ice.
subract q ice from q coke, then solve for deltaT
q(coke) - q(ice) = (4.18 J/gK)(285g)(deltaT)
rethink, not rething. ;-)
thanks!
To determine the final temperature and the amount of ice remaining, you can use the principle of heat transfer. The heat gained by the ice must be equal to the heat lost by the Coke in order to reach thermal equilibrium.
First, let's calculate the heat gained by the ice using the equation:
q_ice = m_ice * c_ice * ΔT
where q_ice is the heat gained by the ice, m_ice is the mass of the ice cube (45g), c_ice is the specific heat capacity of ice (2.09 J/g°C), and ΔT is the change in temperature.
Since the ice is initially at 0°C and will reach thermal equilibrium with the Coke, the final temperature of both the ice and the Coke will be the same (let's call it Tf).
Therefore, the heat gained by the ice can be written as:
q_ice = m_ice * c_ice * (Tf - 0)
Next, we need to calculate the heat lost by the Coke. The heat lost by the Coke can be calculated using the equation:
q_Coke = m_Coke * c_Coke * ΔT
where q_Coke is the heat lost by the Coke, m_Coke is the mass of the Coke (240g), c_Coke is the specific heat capacity of Coke (4.18 J/g°C), and ΔT is the change in temperature.
Since the initial temperature of the Coke is 10.5°C, the change in temperature is Tf - 10.5.
Therefore, the heat lost by the Coke can be written as:
q_Coke = m_Coke * c_Coke * (Tf - 10.5)
Since the system is in thermal equilibrium, the heat gained by the ice must be equal to the heat lost by the Coke. Therefore, we can set up the equation:
q_ice = q_Coke
m_ice * c_ice * (Tf - 0) = m_Coke * c_Coke * (Tf - 10.5)
Now, you can substitute the given values and solve for Tf:
45g * 2.09 J/g°C * Tf = 240g * 4.18 J/g°C * (Tf - 10.5)
Simplifying this equation will give you the final temperature (Tf). Once you have Tf, you can determine if any ice remains by checking if the final temperature is above 0°C. If the final temperature is above 0°C, then all the ice would have melted; otherwise, there would be some ice remaining.
Hope this helps! Let me know if you have any further questions.