Question

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

Answer 1

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"`.