Question

A student drops two metallic objects into a 120-g steel con- tainer holding 150 g of water at 25°C. One object is a 200-g cube of copper that is initially at 85°C, and the other is a chunk of aluminum that is initially at 5.0°C. To the surprise of the student, the water reaches a final temperature of 25°C, precisely where it started. What is the mass of the aluminum chunk?

Answer 1

The mass of the aluminum chunk is 258 g

Step-by-step explanation:

Given;

mass of steel container = 120-g

mass of water = 150 g

initial temperature of water, = 25°C

mass of copper cube,
`M_(cu)` = 200 g

initial temperature of the copper cube,
`T_c_u` = 85°C

initial temperature of the aluminum chunk
`T_A_l` = 5.0°C

Neglecting heat loss, heat exchanged by the two metallic objects is the same since initial temperature is equal to final temperature of water.

`M_(Al)C_(Al) \delta T_(Al) = M_(cu)C_(cu) \delta T_(cu)`

where;

`C_(AL)` is specific heat capacity of aluminum

`\delta T_(Al)` is change in temperature of aluminum

`C_c_u` is the specific heat capacity of copper

`\delta T_c_u` is the change in temperature of copper

`M_(Al)C_(Al) \delta T_(Al) = M_(cu)C_(cu) \delta T_(cu) \\\\M_(Al) = (M_(cu)C_(cu) \delta T_(cu))/(C_(Al) \delta T_(Al)) \\\\M_(Al) = (0.2*387*60)/(900*20) = 0.258 \ kg`

Therefore, the mass of the aluminum chunk is 258 g