Question

Two systems with heat capacities 19.9 J mol-1 K-1 and 28.2 ] mol 1 K-1 respectively interact thermally and come to an equilibrium temperature of 300C. If the initial temperature of system 1 was 450C, what was the initial temperature of system 2 in °C? You may assume that the total energy of the combined systems remains constant

Answer 1

Answer : The initial temperature of system 2 is,
`19.415^oC`

Explanation :

In this problem we assumed that the total energy of the combined systems remains constant.

`-q_1=q_2`

`m* c_1* (T_f-T_1)=-m* c_2* (T_f-T_2)`

The mass remains same.

where,

`C_1` = heat capacity of system 1 = 19.9 J/mole.K

`C_2` = heat capacity of system 2 = 28.2 J/mole.K

`T_f` = final temperature of system =
`30^oC=273+30=303K`

`T_1` = initial temperature of system 1 =
`45^oC=273+45=318K`

`T_2` = initial temperature of system 2 = ?

Now put all the given values in the above formula, we get

`-19.9J/mole.K* (303-318)K=28.2J/mole.K* (303-T_2)K`

`T_2=292.415K`

`T_2=292.415-273=19.415^oC`

Therefore, the initial temperature of system 2 is,
`19.415^oC`