Question

A chunk of tin weighing 18.5 grams and originally at 97.38 °C is dropped into an insulated cup containing 75.7 grams of water at 21.52 °C. Assuming that all of the heat is transferred to the water, the final temperature of the water is ____

Answer 1

Answer:

The final temperature of the water is 22.44°C.

Explanation:

Heat lost by tin will be equal to heat gained by the water

$-q_1=q_2$

Mass of tin = $m_1=18.5 g$

Specific heat capacity of tin = $c_1=0.21 J/g^oC$

Initial temperature of the tin = $T_1=97.38^oC$

Final temperature = $T_2$=T

$q_1=m_1c_1\times (T-T_1)$

Mass of water= $m_2=75.7 g$

Specific heat capacity of water= $c_2=4.184 J/g^oC$

Initial temperature of the water = $T_3=21.52^oC$

Final temperature of water = $T_2$=T

$q_2=m_2c_2\times (T-T_3)$

$-q_1=q_2$  (Law of Conservation of energy)

$-(m_1\times c_1\times (T-T_1))=m_2\times c_2\times (T-T_3)$

On substituting all values:

$-(18.5 g\times 0.21 J/g^oC\times (T-97.38^oC))=75.7 g\times 4.184 J/g^oC\times (T-21.52 ^oC)$

we get, T = 22.44°C

The final temperature of the water is 22.44°C.