# An object with a mass of 1 kg, temperature of 350 ^oC, and a specific heat of 6 J/(kg*K) is dropped into a container with 28 L  of water at 0^oC . Does the water evaporate? If not, by how much does the water's temperature change?

Nov 23, 2017

The water does not evaporate and the change in temperature is $= {0.018}^{\circ} C$

#### 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 $\Delta {T}_{o} = 350 - T$

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

The specific heat of water is ${C}_{w} = 4.186 k J k {g}^{-} 1 {K}^{-} 1$

The specific heat of the object is ${C}_{o} = 0.006 k J k {g}^{-} 1 {K}^{-} 1$

The mass of the object is ${m}_{0} = 1 k g$

The mass of the water is ${m}_{w} = 28 k g$

$1 \cdot 0.006 \cdot \left(350 - T\right) = 28 \cdot 4.186 \cdot T$

$350 - T = \frac{28 \cdot 4.186}{1 \cdot 0.006} \cdot T$

$350 - T = 19634.7 T$

$19635.7 T = 350$

$T = \frac{350}{19635.7} = {0.018}^{\circ} C$

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