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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?

Respuesta :

onyebuchinnaji

Answer:

The mass of the aluminum chunk is 258 g

Explanation:

Given;

mass of steel container =  120-g

mass of water = 150 g

initial temperature of water, = 25°C

mass of copper cube, [tex]M_{cu}[/tex] = 200 g

initial temperature of the copper cube, [tex]T_c_u[/tex] = 85°C

initial temperature of the aluminum chunk [tex]T_A_l[/tex] = 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.

[tex]M_{Al}C_{Al} \delta T_{Al} = M_{cu}C_{cu} \delta T_{cu}[/tex]

where;

[tex]C_{AL}[/tex] is specific heat capacity of aluminum

[tex]\delta T_{Al}[/tex] is change in temperature of aluminum

[tex]C_c_u[/tex] is the specific heat capacity of copper

[tex]\delta T_c_u[/tex] is the change in temperature of copper

[tex]M_{Al}C_{Al} \delta T_{Al} = M_{cu}C_{cu} \delta T_{cu} \\\\M_{Al} = \frac{M_{cu}C_{cu} \delta T_{cu}}{C_{Al} \delta T_{Al}} \\\\M_{Al} = \frac{0.2*387*60}{900*20} = 0.258 \ kg[/tex]

Therefore, the mass of the aluminum chunk is 258 g