What mass of ethyl alcohol will give up 33,000 J of energy as it cools from 27°C to -3°C?

What mass of ethyl alcohol will give up 33,000 J of energy as it cools from 27°C to -3°C?
1. 1.92×109kg
2. 0.453k
3. 0.566kg
4. 2.41x109kg

1 Answer
Meave60
Jun 29, 2018

I would choose answer 2. #"0.473 kg"#.

Explanation:

The equation to use is:

#q=mcDeltaT#,

where:

#q# is energy, #m# is mass, #c# is specific heat capacity, and #DeltaT# is change in temperature. #DeltaT=T_"final"-T_"initial"#

Since specific heat of ethanol was not given, I found it online. It does vary with temperature.

Known

#q=-##"33000 J"# #larr# The negative sign means the energy was released

#c_"EtOH"="2.46 J"/("g"*""^@"C")#
www.chegg.com

#T_"initial"="27"^@"C"#

#T_"final"=-3^@"C"#

#DeltaT=-3^@"C"-"27"^@"C"=-30^@"C"# #larr# A negative #DeltaT# means the temperature decreased.

Unknown

#m#

Solution

Rearrange the equation to isolate #m#. Plug in the known values and solve.

#m=q/(c*DeltaT)#

#m=(-33000color(red)cancel(color(black)("J")))/((2.46color(red)cancel(color(black)("J")))/("g"*""^@color(red)cancel(color(black)("C")))xx-30^@color(red)cancel(color(black)("C")))="447 g"#

Convert to kilograms.

#447color(red)cancel(color(black)("g"))xx("1 kg")/(1000color(red)cancel(color(black)("g")))="0.447 kg"#

I would choose answer 2. #"0.473 kg"#.

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