a 506g piece of copper tubing is heated to 89.5C and placed in an insulated vessel containing 159g of water at 22.8C. Assuming no loss of water and a heat capacity for the vessel of 10.0J/K, what is the final temperature of the system (c of copper = 0.387 J/g*K)?
Q=cm(Tf-Ti)
Q = the heat of an object
m = the mass
c = the heat capacity of the substance
Tf= the final temperature
Ti= the initial temperature
Q gained by water = Q lost by copper
Make sure your units go together.
To find the final temperature of the system, we need to calculate the heat gained by the water, the heat lost by the copper tubing, and equate the two.
Let's calculate the heat gained by the water first, using the equation:
Q = mcΔT
Where:
Q is the heat gained by the water
m is the mass of the water
c is the specific heat capacity of water (which is approximately 4.18 J/g*K)
ΔT is the change in temperature of the water
Given:
m = 159g
c = 4.18 J/g*K
ΔT = Tf - 22.8C (final temperature of the system - initial temperature of the water)
Next, let's calculate the heat lost by the copper tubing:
Q = mcΔT
Where:
Q is the heat lost by the copper tubing
m is the mass of the copper tubing
c is the specific heat capacity of copper (0.387 J/g*K)
ΔT is the change in temperature of the copper tubing
Given:
m = 506g
c = 0.387 J/g*K
ΔT = 89.5C - Tf (initial temperature of the copper tubing - final temperature of the system)
Now, let's set up an equation to equate the heat gained by the water and the heat lost by the copper tubing:
Qwater = -Qcopper
mcwaterΔTwater = -mccopperΔTcopper
159g * 4.18 J/g*K * (Tf - 22.8C) = -506g * 0.387 J/g*K * (89.5C - Tf)
Now, we can solve this equation to find Tf, the final temperature of the system.
159 * 4.18 * (Tf - 22.8) = -506 * 0.387 * (89.5 - Tf)
Simplify and solve for Tf:
663.42Tf - 14318.47 = -195.702Tf + 35413.642
859.122Tf = 49731.112
Tf = 57.9C
Therefore, the final temperature of the system is approximately 57.9°C.