Question

`"2659 J"` of heat energy are required to heat a substance with a mass of `"24.25 g"` from `"23.7"^@"C"` to `"163.5"^@"C"`. What is its specific heat capacity?

Answer 1

The specific heat capacity is `784.3 J/(C·kg)`.

Explanation:

So, the equation we are using is `Q = mcDeltaT`.

=> Where `Q` is the amount of thermal energy in joules, `J`.
=> Where `m` is the mass in kilograms, `kg`.
=> Where `c` is the specific heat capacity.
=> Where `DeltaT` is the change in temperature in degrees Celsius.

`24.25 g = 0.02425 kg`

`Q = mcDeltaT`

`Q = mc (T_2-T_1)`

`"2659 J" = "0.02425 kg"xxcxx"(163.5 - 23.7) °C"`

`"2659 J" = "0.02425 kg"xxcxx"139.8 °C"`

`"19.02 J/°C"= "0.02425 kg"xxc`

`c = "784.3 J/(°C·kg)"`

The specific heat capacity is `784.3 J/(°C·kg)`.

Hope this helps :)

Answer 2

The specific heat is `0.7843"J"/("g"*^@"C")`.

Explanation:

Apply the equation `Q=mcDeltaT`, where `Q` is the energy in Joules, `m` is the mass in grams, `c` is the specific heat, and `DeltaT` is change in temperature. `DeltaT=T_"final"-T_"initial"`

Known
`Q="2659 J"`
`m="24.25 g"`
`T_"initial"="23.7"^@"C"`
`T_"final"="163.5"^@"C"`
`DeltaT="163.5"^@"C"-"23.7"^@"C"="139.8"^@"C"`

Unknown
`c`

Solution
Rearrange the equation `Q=mcDeltaT` to isolate `c`. Substitute the known values into the equation and solve.

`c=(Q)/(m*DeltaT)`

`c=(2659"J")/(24.25"g"*139.8^@"C")`

`c=0.7843"J"/("g"*^@"C")`