Question

1. define the following variables.

q = energy transfer
m = mass of the material
e = specify heat capacity
p = rate of energy transfer
δt = change in time
k = thermal conductivity
a = area
l = thickness of material
δt = diff in temp
(18 - 22) a 1.00kg piece of aluminum metal at 90.0°c is placed in 4.00 liters (=4.00 kg) of water at 25.0°c. determine the final temperature (tf).

1. list all known values.
2. list all unknown values.
3. select equations.
4. apply known values.
5. solve.

Explanation:

Step1: Write the heat - transfer equation

According to the principle of conservation of energy, the heat lost by the aluminum \(Q_{Al}\) is equal to the heat gained by the water \(Q_{w}\). The heat - transfer formula is \(Q = mc\Delta T\), where \(m\) is the mass, \(c\) is the specific heat capacity, and \(\Delta T=T_{f}-T_{i}\) (for water) or \(T_{i}-T_{f}\) (for aluminum). So, \(m_{Al}c_{Al}(T_{Al}-T_{f})=m_{w}c_{w}(T_{f}-T_{w})\)

Step2: Substitute the known values

We know that \(m_{Al} = 1.00\space kg\), \(c_{Al}=0.900\times10^{3}\space J/(kg\cdot^{\circ}C)\), \(T_{Al} = 90.0^{\circ}C\), \(m_{w}=4.00\space kg\), \(c_{w}=4.18\times 10^{3}\space J/(kg\cdot^{\circ}C)\), \(T_{w}=25.0^{\circ}C\)

Substitute these values into the equation:

$$
LATEXBLOCK0
$$

Answer:

The final temperature \(T_{f}\approx28.3^{\circ}C\)