# An object with a mass of 4 g is dropped into 650 mL of water at 0^@C. If the object cools by 300 ^@C and the water warms by 2 ^@C, what is the specific heat of the material that the object is made of?

Nov 20, 2017

The specific heat is $= 4.53 k J k {g}^{-} 1 {K}^{-} 1$

#### Explanation:

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

For the cold water,  Delta T_w=2ºC

For the object DeltaT_o=300ºC

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

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

Let, ${C}_{o}$ be the specific heat of the object

The mass of the object is $m = 0.004 k g$

$0.004 \cdot {C}_{o} \cdot 300 = 0.650 \cdot 4.186 \cdot 2$

${C}_{o} = \frac{0.650 \cdot 4.186 \cdot 2}{0.004 \cdot 300}$

$= 4.53 k J k {g}^{-} 1 {K}^{-} 1$