Question

Fifteen grams of substance X at 95 degrees Celsius is mixed with 45 grams of substance Z at 85 degrees Celsius in a container which was originally at 25 degrees Celsius. Neglecting any transfer of heat to the environment, the temperature at the end of 15 minutes was 32 degrees Celsius. What is the equilibrium temperature?
A. 95 degrees Celsius
B. 85 degrees Celsius
C. 32 degrees Celsius
D. 25 degrees Celsius

Answer 1

According to the Law of Conservation of Energy, energy is neither created nor destroyed. They are just transferred from one system to another. To obey this law, the energy of the substances inside the container must be equal to the substance added to it. The energy is in the form of heat. There can be two types of heat energy: latent heat and sensible heat. Sensible heat is energy added or removed when a substance changes in temperature. Latent heat is the energy added or removed at a constant temperature during a phase change. Since there is no mention of phase change, we assume the heat involved here is sensible heat. The equation for sensible heat is:

H = mCpΔT
where
m is the mass of the substance
Cp is the specific heat of a certain type of material or substance
ΔT is the change in temperature.

So the law of conservation of heat tells that:

Sensible heat of Z + Sensible heat of container = Sensible heat of X

Since we have no idea what these substances are, there is no way of knowing the Cp. We can't proceed with the calculations. So, we can only assume that in the duration of 15 minutes, the whole system achieves equilibrium. Therefore, the equilibrium temperature of the system is equal to 32°C. The answer is C.