# An object with a mass of 3 kg, temperature of 173 ^oC, and a specific heat of 23 J/(kg*K) is dropped into a container with 32 L  of water at 0^oC . Does the water evaporate? If not, by how much does the water's temperature change?

Jul 25, 2017

The water does not evaporate and the change in temperature is $= {0.09}^{\circ} C$

#### Explanation:

The heat is transferred from the hot object to the cold water.

Let $T =$ final temperature of the object and the water

For the cold water, $\Delta {T}_{w} = T - 0 = T$

For the object $\Delta {T}_{o} = 173 - T$

${m}_{o} {C}_{o} \left(\Delta {T}_{o}\right) = {m}_{w} {C}_{w} \left(\Delta {T}_{w}\right)$

${C}_{w} = 4.186 k J k {g}^{-} 1 {K}^{-} 1$

${C}_{o} = 0.023 k J k {g}^{-} 1 {K}^{-} 1$

$3 \cdot 0.023 \cdot \left(173 - T\right) = 32 \cdot 4.186 \cdot T$

$173 - T = \frac{32 \cdot 4.186}{3 \cdot 0.023} \cdot T$

$173 - T = 1941.3 T$

$1942.3 T = 173$

$T = \frac{173}{1942.3} = {0.09}^{\circ} C$

As $T < {100}^{\circ} C$, the water does not evaporate