Question

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

Answer 1

0.396 BTU

Explanation:

Convert 10 grams to pounds:
`10 * 0.0022 = 0.022` pound

Convert 50 degrees C to Fahrenheit:
`(50 * 9 / 5) + 32 = 122` degrees Fahrenheit

Convert 40 degrees C to Fahrenheit:
`(40 * 9/5) + 32 = 104` degrees Fahrenheit

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

Heat lost in British Thermal Units (BTU):
`0.022 * 18 = 0.396` BTU

Answer 2

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

In your problem,

`m = "10 g"`
`c = "4.184 J·K"^"-1""g"^"-1"`
`ΔT = T_"f" - T_"i" = "40 °C - 50 °C = -10 °C"`

∴ `q = "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"`

The negative sign tells you that energy is being given off.