A block of mass m₁, specific heat c₁, and temperature T₁ is brought into contact with a block of another material, of mass, specific heat, and temperature, respectively, m₂, c₂, and T₂. After reaching thermal equilibrium between the blocks, if c₁ and c₂ are constants, and assuming that the heat transfer with the environment is negligible, calculate the final equilibrium temperature T.

Three liquids A, B, and C are at 10 °C, 24 °C, and 40 °C, respectively. It is known that:
a) Mixing equal masses of A and B, the final temperature is 14 °C;
b) Mixing masses of A and C in the ratio of m_A:m_C = 2:3, the final temperature is 30 °C.
Calculate what will be the equilibrium temperature of the mixture of B and C in the ratio of m_B:m_C = 1:2.

In what ratio must a certain mass M of water be divided initially at 20°C, under normal atmospheric pressure, assuming that all the energy taken from the part that freezes is used to evaporate the other part? Data:
Specific heat of water: 1 cal/g °C;
Latent heat of vaporization of water: 540 cal/g;
Latent heat of solidification of water: −80 cal/g.

In a container thermally insulated from the environment a mixture of ice and water is placed at 0 °C at atmospheric pressure. By supplying a certain amount of energy by heat to the mixture, we verify that the temperature of the mixture does not change and the volume of the system decreases by 0.5 cm³.
a) Calculate the mass of ice that turns into liquid water;
b) Determine the amount of energy by heat received in the mixture.
Data: density of ice 0.92 g/cm³, the density of water 1 g/cm³, and latent heat of fusion of ice 80 cal/g.

A young man bought a ring that claimed to have 9 grams of gold and 1 gram of copper. To prove the information, the boy, a physics student, heated the ring (which had 10 grams of mass) to 520 °C, which he knew was lower than the melting point of the two metals. He placed the ring in a calorimeter with a heat capacity of 20 cal/°C and which contained 80 grams of water at 18°C. The thermal equilibrium was verified at 20 °C. Assuming that the specific heats in the alloy are 0.09 cal/g°C for copper and 0.03 cal/g°C for gold, determine the masses of copper and gold in the ring.

A meteorite of mass 10 kg, when penetrating the Earth's atmosphere in a course of 3 km, has its speed reduced from 400 m/s to 200 m/s, due to air resistance. The trajectory can be considered a straight line. Considering the energy radiated by the meteorite to be negligible and its thermal conductivity perfect, determine:
a) The average force that acted on the meteorite;
b) The heat generated by friction during entry into the atmosphere;
c) Assuming all the heat produced is absorbed by the meteorite, and its initial temperature is 100 K, what is its final temperature?
Data:
Specific heat of the meteorite material: c = 0.1 kcal/kg.K and 1 kcal = 4200 J.