# How much heat is given off when 10 grams of water are cooled from 50°C to 40°C?

Oct 12, 2016

0.396 BTU

#### Explanation:

Convert 10 grams to pounds:
$10 \cdot 0.0022 = 0.022$ pound

Convert 50 degrees C to Fahrenheit:
$\left(50 \cdot \frac{9}{5}\right) + 32 = 122$ degrees Fahrenheit

Convert 40 degrees C to Fahrenheit:
$\left(40 \cdot \frac{9}{5}\right) + 32 = 104$ degrees Fahrenheit

Calculate the change in temperature:
$122 - 104 = 18$ degrees Fahrenheit

Heat lost in British Thermal Units (BTU):
$0.022 \cdot 18 = 0.396$ BTU

Oct 13, 2016

The process will give off 420 J of heat.

#### Explanation:

The energy $q$ required to heat an object is given by the formula

color(blue)(bar(ul(|color(white)(a/a)q = mcΔTcolor(white)(a/a)|)))" "

where

$m$ is the mass
$c$ is the specific heat capacity
ΔT is the change in temperature

$m = \text{10 g}$
$c = \text{4.184 J·K"^"-1""g"^"-1}$
ΔT = T_"f" - T_"i" = "40 °C - 50 °C = -10 °C"
$q = \text{10" color(red)(cancel(color(black)("g"))) × "4.184 J"·color(red)(cancel(color(black)("K"^"-1""g"^"-1"))) × ("-10" color(red)(cancel(color(black)("°C")))) = "-420 J}$