Question

A 25.0 g sample of a metal at 87.7 deg C is placed in 37.4 g of water at 10.3 deg C, and the final temperature of the system is 15.4 deg C. Calculate the specific heat of the metal in J/g°C.

A) 0.387 J/g°C
B) 0.104 J/g°C
C) 0.621 J/g°C
D) 0.815 J/g°C

Answer 1

To find the specific heat capacity of the metal, apply the principle of conservation of energy. The specific heat is calculated using the mass and temperature change of the metal and water, along with the known specific heat of water.OPTION A.

Step-by-step explanation:

The student is asking about the calculation of the specific heat capacity of a metal using the method of mixtures where the metal and water reach thermal equilibrium. The concept is based on conservation of energy, where the heat lost by the hot metal is equal to the heat gained by the cooler water. The equation q=mc∆T can be used, where 'q' is the heat transfer, 'm' is the mass, 'c' is the specific heat, and ∆T is the change in temperature.

Using the given data, assume that the heat lost by the metal (q_metal) is equal to the heat gained by the water (q_water). Hence, q_metal = q_water.

To find the specific heat (c_metal) of the metal: c_metal = (m_water × c_water × (T_final - T_initial_water)) / (m_metal × (T_initial_metal - T_final)). The mass and initial and final temperatures are known, while the specific heat of water is typically 4.18 J/g°C.

By plugging in the values: c_metal = (37.4g × 4.18 J/g°C × (15.4°C - 10.3°C)) / (25.0g × (87.7°C - 15.4°C)). Calculate the specific heat from this equation.