Iron weights weighing 100 and 200 g, taken at room temperature, were immersed for a long time in boiling water.

Iron weights weighing 100 and 200 g, taken at room temperature, were immersed for a long time in boiling water. Has the internal energy of the weights changed in this case? If so, which of them will have a greater change in internal energy?

Given:

m1 = 100 grams = 0.1 kilograms – the mass of the first iron weight;

m2 = 200 grams = 0.2 kilograms – the mass of the second iron weight;

t0 is the temperature of both iron weights (room temperature).

It is required to determine in which of the weights the internal energy has changed more after being placed in boiling water.

Let the temperature of the boiling water be t. Since, according to the condition of the problem, the iron weights were placed in water for a long time, we assume that the temperature of the weights also became equal to t, that is, they heated up by dt = t – t0.

Then, the internal energy of the first weight changed by an amount equal to:

Q1 = m1 * c * dt = 0.1 * c * dt, where c is the heat capacity of iron.

The internal energy of the second weight changed by an amount equal to:

Q2 = m2 * c * dt = 0.2 * c * dt.

Since Q2> Q2 (0.2 * c * dt> 0.1 * c * dt), the internal energy of the second weight has changed more.

Answer: for a weight with a larger mass, the internal energy has changed more.