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.

1 Answer
MetaPhysik
Jan 4, 2018

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.

Related questions
See all questions in Latent Heat
Impact of this question
3057 views around the world
You can reuse this answer
Creative Commons License