# Question #d4bcc

Apr 22, 2014

The thermochemistry base equation is $Q = m {C}_{p} T$ where
Q = Heat in Joules
m = mass of the material
${C}_{p}$ = specific heat capacity
T = change in Temperature ${T}_{f} - {T}_{i}$

For this equation the metal is going to lose heat make Q negative while the water is going to gain heat making Q positive

Due to the Law of Conservation of Energy the heat lost by the metal will be equal to the heat gained by the water.

$- {Q}_{P b} = + {Q}_{w a t e r}$

specific heat of lead is 0.130 j/gC
specific heat of water is 4.18 j/gC

$- \left[800 g \left(100 - 900 C\right) \left(.130 \frac{J}{g} C\right)\right] = 1500 g \left(100 - {T}_{i} C\right) \left(4.18 \frac{J}{g} C\right)$
$83 , 200 = 62 , 700 - 6 , 270 {T}_{i}$
$20 , 500 = - 6270 {T}_{i}$
$- 3.29 C = {T}_{i}$

Change in temp for the water is $100 - \left(- 3.29\right) C = 103.29 C$