# Question 37748

Apr 9, 2015

The final temperature of the system will be $\text{32"^@"C}$.

Before doing any actual calculations, try to predict what's going to happen when you place the silver piece in water.

Since the silver is hotter than the water, you'd predict that the water will heat up and the silver will cool down.

You need to know the specific heat of silver and water

c_("silver") = "0.240 J/g"^@"C"
c_("water") = "4.18 J/g"^@"C"

The principle is very simple - the heat lost by the silver while cooling down will be equal to the heat gained by the water while heating up.

$- {q}_{\text{silver") = q_("water}}$ $\to$ the minus sign designates heat lost;

The equation that links heat gained or lost and change in temperature is

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

$m$ - the mass of the substance;
$c$ - the specific heat of the substance;
$\Delta T$ - the change in temperature - defined as the difference between the final and initial temperatures of the substance.

Because the system will reach equilibrium, the final temperature for the silver will be equal to the final temperature of the water.

Since you know that what is lost by the silver must be gained by the water, you can write

$- {m}_{\text{silver") * c_("silver") * DeltaT_("silver") = m_("water") * c_("water") * DeltaT_("water}}$

$- 20 \cancel{\text{g") * 0.240cancel("J")/(cancel("g") * ^@cancel(C)) * (color(red)(T_("final")) - 350)^@cancel("C") = 200cancel("g") * 4.18cancel("J")/(cancel("g") * ^@cancel("C")) * (color(red)(T_("final")) - 30)^@cancel("C}}$

To get rid of the minus sign, you can write $\left({T}_{\text{final}} - 350\right)$ as $- \left(350 - {T}_{\text{final}}\right)$, which will give you

$4.8 \left(350 - \textcolor{red}{{T}_{\text{final"))) = 836 * (color(red)(T_("final}}} - 30\right)$

Solve for ${T}_{\text{final}}$ to get

T_("final") = 2670/840.8 = 31.83"^@C#

Rounded to two sig figs, the answer will be

${T}_{\text{final") = color(green)("32"^@"C}}$

SIDE NOTE According to your data, the correct number of sig figs for the answer should be one; however, rounding the answer to one sig figs would make the final temperature equal to 30 degrees Celsius, which is the starting temperature of the water.

I'll leave the answer with two sig figs, but take note that sig figs are very important to an answer.

The video discusses how to solve a sample calorimetry calculation.

Video from: Noel Pauller