I am having a horrible time with Enthalpy change. I understand how to find specific heat I believe, but the heat capacity of the vessel is given as 10 J/K. My problem is that my professor did not show us how to work this type of problem, and I desperately need help with it. Here is the following problem. I am trying to find the final temperature of the system. I feel like I am missing something, PLEASE HELP!
A 670. g piece of copper tubing is heated to 97.1°C and placed in an insulated vessel containing 57.5 g of water at 40.0°C. Assuming no loss of water and heat capacity for the vessel of 10.0 J/K, what is the final temperature of the system (c of copper = 0.387 J/g·K)?
heat lost by Cu + heat gained by water + heat gained by calorimeter = 0
[massCu x specific heat Cu x (Tfinal-Tinitial)] + [mass water x specific heat water x (Tfinal-Tinitial)] + [10 x (Tfinal-Tinitial)] = 0
Solve for Tfinal, the only unknown.
Thankyou, that helped so much.
To find the final temperature of the system, you need to consider the heat gained by the water, the heat lost by the copper tubing, and the heat absorbed by the vessel.
First, let's calculate the heat gained by the water. The equation used to calculate heat gained or lost is:
q = mcΔT
where q is the heat gained or lost, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.
For the water:
m_water = 57.5 g
c_water = 4.18 J/g·K (specific heat capacity of water)
ΔT_water = final temperature - initial temperature = final temperature - 40.0°C
Now, let's calculate the heat lost by the copper tubing:
m_copper = 670 g
c_copper = 0.387 J/g·K (specific heat capacity of copper)
ΔT_copper = final temperature - initial temperature = final temperature - 97.1°C
Next, let's calculate the heat absorbed by the vessel:
c_vessel = 10.0 J/K (heat capacity of the vessel)
The total heat gained by the water is equal to the total heat lost by the copper tubing and absorbed by the vessel:
q_water = q_copper + q_vessel
Now we can set up the equation:
m_water * c_water * ΔT_water = m_copper * c_copper * ΔT_copper + c_vessel * ΔT_copper
Plugging in the given values, the equation becomes:
(57.5 g) * (4.18 J/g·K) * (final temperature - 40.0°C) = (670 g) * (0.387 J/g·K) * (final temperature - 97.1°C) + (10.0 J/K) * (final temperature - 97.1°C)
Now, you can solve this equation for the final temperature of the system. Rearrange the equation and calculate the final temperature. Note that the temperatures used in the equation need to be converted to Kelvin by adding 273.15:
(57.5 g) * (4.18 J/g·K) * (final temperature - 40.0°C) = (670 g) * (0.387 J/g·K) * (final temperature - 97.1°C) + (10.0 J/K) * (final temperature - 97.1°C)
Once you have the final temperature, subtract 273.15 to convert it back to Celsius.