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
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.