Question

If 65.34g piece of tin were to lose 754 Joules of energy in a calorimeter while experiencing a temperature change from 23.9 degrees C to 22.0 degrees C, how would you find its specific heat?

Answer 1

The values you provided are way off.

Explanation:

SIDE NOTE First thing first, the values you provided are very inaccurate. Using these values will produce an impossible result for the specific heat of tin, approximately `30` times bigger than what its real value is.

WIth this being said, I will assume that the piece of tin lost `"75.4 J"`, instead of `"754 J"`. The result will not be ideal, but it will be closer to reality.

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The question wants you to determine tin's specific heat.

Before doing any calculation, try to get a clear understanding of what you need to determine.

A substance's specific heat tells you the amount of heat needed to increase the temperature of `"1 g"` of that substance by `1^@"C"`.

In your case, a mroe accurate description would sound like this - the amount of heat that must be lost by `"1 g"` of a substance to decrease its temperature by `1^@"C"`.

The equation that establishes a relationship between heat lost and change in temperature looks like this

`color(blue)(-q = m * c * DeltaT)" "`, where

`-q` - heat lost by the metal
`m` - the mass of the metal
`c` - its specific heat
`DeltaT` - th change in temperature, defined as final temperature minus initial temperature

The trick here is to realize that when heat is being lost by the system, `q` will have a negative value. In this case, `"75.4 J"` are being lost, so `q` will be

`q = -"75.4 J"`

Since you have all the information you need to find the specific heat of tin, plug in your values in the above equation and solve for `c`

`c = (-q)/(m * DeltaT)`

`c = (-(-"75.4 J"))/("65.34 g" * (22.0 - 23.9)^@"C") = color(green)(0.607"J"/("g" ""^@"C"))`

The actual specific heat of tin is `0.21"J"/("g" ""^@"C")`, so I recommend double-checking the values you have.