In an aluminum calorimeter weighing 140 g, 250 g of water was poured at a temperature of 15C.

In an aluminum calorimeter weighing 140 g, 250 g of water was poured at a temperature of 15C. After a metal bar with a mass of 100 g, heated to 100C, was placed in a calorimeter with water, a temperature of 16C was established there. What metal is the bar made of?

Let the mass of the aluminum calorimeter be m1 = 140 g = 0.14 kg, and the mass of water m2 = 250 g = 0.25 kg, and the mass of the metal bar m3 = 100 g = 0.1 kg. The temperature of the calorimeter and water coincides T1 = T2 = 15 C0, and the temperature of the bar T3 = 100 C0. Final temperature T = 16 C0. It is known that the specific heat capacity of aluminum and water is C1 = 920 J / kg * C0, C2 = 4200 J / kg * C0.

According to the law of conservation of energy: Q = C * m * ∆T, Q1 + Q2 + Q3 = 0.

Q1 = C1 * m1 * (T – T1), Q2 = C2 * m2 * (T – T2), Q3 = C3 * m3 * (T – T3).

T – T1 = 16 C0 – 15 C0 = 1 C0.

T – T3 = 16 C0 – 100 C0 = -84 C0.

Substitute the quantities in the equation and calculate.

920 J / kg * C0 * 0.14 kg * 1 C0 + 4200 J / kg * C0 * 0.25 kg * 1 C0 – C3 * 0.1 kg * 84 C0 = 0.

128.8 J + 1050 J – 8.4 C3 = 0.

C3 = 1178.8 / 8.4 J.

C3 = 140, (3) J.

Answer: C3 ≈ 140 J, lead.