Two substances of the same mass were mixed in a calorimeter. It is known that the temperature of the first

Two substances of the same mass were mixed in a calorimeter. It is known that the temperature of the first substance increased twice as a result, and that of the second it dropped three times. It is known that the specific heat capacity of the first c1 = 1000 J / kg * K. Find the specific heat of the second substance. You should get 250 J / kg * K

Let us denote the steady-state equilibrium temperature by T. Each of the substances has a mass m. The heat capacity of the first substance is c1 = 1000 J / kg * K, the second is c2.

The temperature before mixing for the first substance is T / 2, the second 3T.

Heat balance equation:

c1m (T / 2) + 3c2mT = c1mT + c2mT.

We multiply both sides of the equation by 2, and also divide by T and by m:

c1 + 6c2 = 2c1 + 2c2;

4c2 = c1;

c2 = c1 / 4 = (1000 J / kg * K) / 4 = 250 J / kg * K.

Answer: The heat capacity of the second substance is 250 J / kg * K.