Question

Infer When one object heats another, does the temperature increase of one object always equal the temperature decrease of the other object? Explain.

Answer 1

Answer:

No

Explanation:

When one object heats another, the amount of heat transferred by the hotter object ($Q_h$) to the colder object is equal to the amount of heat absorbed by the colder object ($Q_c$):

$Q_h=Q_c$

The two amounts of heat can be written as:

$Q_h=m_h C_h \Delta T_h$

where

$m_h$ is the mass of the hotter object

$C_h$ is the specific heat capacity of the hotter object

$\Delta T_h$ is the change in temperature of the hotter object

And

$Q_c=m_c C_c \Delta T_c$

where

$m_c$ is the mass of the colder object

$C_c$ is the specific heat capacity of the colder object

$\Delta T_c$ is the change in temperature of the colder object

So we can write

$m_h C_h \Delta T_h = m_c C_c \Delta T_c$

or

$\frac{\Delta T_h}{\Delta T_c}=\frac{m_c C_c}{m_h C_h}$

We see that this ratio is not always equal to 1, since the two objects can have different masses and specific heat capacities: therefore, the changes in temperature are not equal.