Question

What is the mass of the salt required to store heat?

A tank of Glauber's salt is in a household. Its purpose is to store `2.8 xx 10^9 J` of heat energy, and it can be heated from `22^@C` to `50^@C`. The melting point of the salt is `32 ^@C` and it has a `L_"f"` (specific latent heat of fusion) of `241 (kj)/(kg)`. Its specific heat capacity in solid state is `1066 J/(kj ^@C)` and in liquid state is `1576 J/(kj ^@C)`.

This is all the information given. Please tell me how you get the values and the process to solving it. Thank you.

Answer 1

Solve for the mass using the heat equation

Explanation:

m = mass
s = specific heat
Q = total heat absorbed = `2.8 xx10^9J`
`T_i,T_m,T_f` are initial, melting and final temperature respectively.

1) Salt absorbs heat when its temperature rises, i.e. , `msDeltaT`
2) While melting, it absorbs heat without temperature change i.e., `mL_f`.

Put these two together:
Total heat gained = Heat gained by salt from `22^o ->32^o`, heat gained while melting + heat gained from `32^o->50^o`

`Q= ms_"solid"(T_m-T_i)+mL_f+ms_"liquid"(T_f-T_m)`
`Q=m{s_"solid"(T_m-T_i)+L_f+s_"liquid"(T_f-T_m)}`

Then solve for the mass.