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.

$-q_1=q_2$

$m\times c_1\times (T_f-T_1)=-m\times c_2\times (T_f-T_2)$

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

$-19.9J/mole.K\times (303-318)K=28.2J/mole.K\times (303-T_2)K$

$T_2=292.415K$

$T_2=292.415-273=19.415^oC$

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