Question

measuring temperature change
when using a calorimeter, the initial temperature of a metal is 70.4°c. the initial temperature of the water is 23.6°c
at the end of the experiment, the final equilibrium temperature of the water is 29.8°c
what is the final temperature of the metal?
what is the temperature change of the water?
what is the temperature change of the metal?

Explanation:

Step1: Determine the final temperature of the metal

In a calorimeter, at equilibrium, the final temperature of the metal is the same as the final temperature of the water.
So, the final temperature of the metal \(T_{m,f}=29.8^{\circ}C\)

Step2: Calculate the temperature change of the water

The formula for temperature change is \(\Delta T = T_{f}-T_{i}\)
For water, \(T_{w,i} = 23.6^{\circ}C\) and \(T_{w,f}=29.8^{\circ}C\)
\(\Delta T_{w}=T_{w,f}-T_{w,i}=29.8 - 23.6=6.2^{\circ}C\)

Step3: Calculate the temperature change of the metal

For metal, \(T_{m,i} = 70.4^{\circ}C\) and \(T_{m,f}=29.8^{\circ}C\)
Using \(\Delta T = T_{f}-T_{i}\), \(\Delta T_{m}=T_{m,f}-T_{m,i}=29.8 - 70.4=- 40.6^{\circ}C\)

Answer:

The final temperature of the metal: \(29.8^{\circ}C\)
The temperature change of the water: \(6.2^{\circ}C\)
The temperature change of the metal: \(-40.6^{\circ}C\)