# Question b4e85

Jul 12, 2015

The initial temperature was $20.2 \text{^@"C}$.

#### Explanation:

Once again, you need to know the specific heat of nickel before doing any calculations.

The specific heat of nickel is listed as being

c_"nickel" = 0.44"J"/("g" ^@"C")

In order to find the initial temperature of the sample, you'll use this equation

$q = m \cdot c \cdot \Delta T$, where

$q$ - the amount of energy in the form of heat absorbed/released;
$m$ - the mass of the sample;
$c$ - the specific heat of the substance;
$\Delta T$ - the change in temperature, defined as ${T}_{\text{final" - T_"initial}}$.

This time, you know that you supplied a certain amount of heat to the sample, 82.9 J to be precise, and that its final temperature was measured at ${35.7}^{\circ} \text{C}$.

You can use the values given to you to dolve for the initial temperature of the sample by

$q = m \cdot c \cdot {\underbrace{\Delta T}}_{\textcolor{b l u e}{{T}_{\textrm{f \in a l}} - {T}_{\text{initial}}}}$

$82.9 \cancel{\text{J") = 12.2cancel("g") * 0.44cancel("J")/(cancel("g") cancel(""^@"C")) * (35.7 - T_"initial")cancel(""^@"C}}$

$82.9 = 191.6 - 5.368 \cdot {T}_{\text{initial}}$

${T}_{\text{initial" = (191.6 - 82.9)/5.368 = 20.249""^@"C}}$

Rounded to three sig figs, the answer will be

T_"initial" = color(green)(20.2""^@"C")#