Question

A 36 g aluminum spoon (specific heat 0.904 J/g·°C) at 25°C is placed in 181 mL (180. g) of coffee at 86°C and the temperature of the two become equal.

(a) What is the final temperature (in °C) when the two become equal? (Assume that coffee has the same specific heat as water, 4.1801 J/g·°C.)
(b) The first time a student solved this problem she got an answer of 89°C. Explain why this is clearly an incorrect answer.

Answer 1

(a) The final temperature is
`83.47^oC`

(b) This is not possible because the final temperature can not be more than the starting temperature of the coffee.

Explanation :

(a) Heat gained by the Al = Heat lost by the coffee

`q_1=-q_2`

`m_1* c_1* (T_f-T_1)=-m_2* c_2* (T_f-T_2)`

where,

`c_1` = specific heat of Al =
`0.904J/g^oC`

`c_2` = specific heat of coffee =
`4.1801J/g^oC`

`m_1` = mass of Al = 36 g

`m_2` = mass of coffee = 180 g

`T_f` = final temperature = ?

`T_1` = initial temperature of Al =
`25^oC`

`T_2` = initial temperature of coffee =
`86^oC`

Now put all the given values in the above formula, we get

`36g* 0.904J/g^oC* (T_f-25)^oC=-180g* 4.1801J/g^oC* (T_f-86)^oC`

`T_f=83.47^oC`

Thus, the final temperature is
`83.47^oC`

(b) As per question, the first time a student solved this problem she got an answer of 89°C that means the final temperature is higher than the starting temperature of the coffee.

So, this is not possible because the final temperature can not be more than the starting temperature of the coffee.