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

2 Answers
John P
Oct 12, 2016

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

Ernest Z.
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

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.

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