Question

The temperature of an object is changed when heat is added to or extracted from it. Determine the final temperature (in °C) of a 90.0 g mass of iron initially at 72.0°C if 1,100 J of heat energy is extracted from it. The specific heat of iron is 448 J/(kg*°C).
1. How is the heat extracted from the sample related to the mass, specific heat, and temperature change?
2. Knowing the initial temperature and the change in temperature, how can you determine the final temperature?
3. What sign (positive or negative) should be associated with the value of Q when heat is extracted?
4. Do you expect the temperature to increase or decrease? Don't forget to change the mass from grams to kilograms. °C

Answer 1

Answer:

$T_f=44.72^{\circ}C$

1. Heat extracted from mass as given by the above equation (1) i.e. heat transfer is directly proportional to mass, temperature change and specific heat.

2. Using the equation of heat as mentioned in eq. (1) we find the value of final temperature.

3. The heat extracted from the system is taken as negative.

4. When heat is extracted from a body then its temperature can be expected to decrease.

Explanation:

Given:

• initial temperature of the iron object, $T_i=72^{\circ}C$

• mass of the object, $m=0.09\ kg$

• heat extracted from the object, $Q=-1100\ J$

• specific heat of iron, $c=448\ J.kg^{-1}.K^{-1}$

From the equation of heat:

$Q=m.c.(T_f-T_i)$ .......................(1)

$-1100=0.09\times 448\times (T_f-72)$

$T_f=44.72^{\circ}C$

1. Heat extracted from mass as given by the above equation (1) i.e. heat transfer is directly proportional to mass, temperature change and specific heat.

2. Using the equation of heat as mentioned in eq. (1) we find the value of final temperature.

3. The heat extracted from the system is taken as negative.

4. When heat is extracted from a body then its temperature can be expected to decrease.