# An object with a mass of 8 g is dropped into 50 mL of water at 0^@C. If the object cools by 5 ^@C and the water warms by 70 ^@C, what is the specific heat of the material that the object is made of?

Dec 8, 2017

Thespecific heat is $= 366.3 k J k {g}^{-} 1 {K}^{-} 1$

#### Explanation:

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

For the cold water,  Delta T_w=70ºC

For the object DeltaT_o=5ºC

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

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

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

The mass of the object is ${m}_{o} = 0.008 k g$

The mass of the water is ${m}_{w} = 0.050 k g$

$0.008 \cdot {C}_{o} \cdot 5 = 0.050 \cdot 4.186 \cdot 70$

${C}_{o} = \frac{0.050 \cdot 4.186 \cdot 70}{0.008 \cdot 5}$

$= 366.3 k J k {g}^{-} 1 {K}^{-} 1$