A 100-g block of iron at 31°C is submerged in 50 g of water at 25°C in a thermally insulated container. If the temperature of the system reaches equilibrium at 26°C, what is the specific heat of iron? (Note: The specific heat of water is 4.2 J/(g⋅°C).)

Question

A 100-g block of iron at 31°C is submerged in 50 g of water at 25°C in a thermally insulated container.  If the temperature of the system reaches equilibrium at 26°C, what is the specific heat of iron?  (Note:  The specific heat of water is 4.2 J/(g⋅°C).)

Quizplus · Accepted Answer

11ecba2d_1300_643a_a3bf_f19e3a54e0ef_MD0008_00 The specific heat of a substance is an intrinsic property (does not depend on mass) and is the amount of heat required to increase a unit mass (1 g or 1 kg) by 1°C or 1 K. The total amount of heat gained or lost by an object is the product of its mass m, its specific heat c, and the change in temperature ΔT, as given by the calorimetry equation: 11ecba2d_1300_643b_a3bf_95e60afa2bb6_MD0008_00 Because the block of iron is hotter than the water, heat flows from the iron to the water, and the temperature of the water increases from 25°C to 26°C (ΔT = 1°C). The heat gained by water is calculated using its given mass (50 g), specific heat 11ecba2d_1300_643c_a3bf_9d18499f0ec8_MD0008_00 11ecba2d_1300_643d_a3bf_cd552bdccac3_MD0008_00 Because the container is thermally insulated, the heat gained by the water is equal to the heat lost by the iron block, q_iron = −210 J. According to the question, the 100-g iron block decreases in temperature from 31°C to 26°C (ΔT = −5°C). The specific heat of iron is calculated by rearranging the calorimetry equation and using these values: 11ecba2d_1300_8b4e_a3bf_0df105c59b84_MD0008_00 11ecba2d_1300_8b4f_a3bf_e1fe8dc25abe_MD0008_00 (Choice B) The amount of heat transferred depends on the change in temperature ΔT, not the initial temperature of the substance. If the initial temperatures of iron (31°C) and water (25°C) are incorrectly used, c_iron = 1.7 J/(g⋅°C). (Choice C) Whereas the specific heat (c) of a substance is an intrinsic property, its heat capacity (C) is the amount of heat required to raise a given amount of the substance (mass) by 1°C. The heat capacity of the iron block is the product of specific heat and mass: 11ecba2d_1300_8b50_a3bf_31307c58d62b_MD0008_00 (Choice D) If the heat capacity of iron is incorrectly determined by using the initial temperatures of the iron block and water, it is calculated as 170 J/°C. Educational objective: The amount of heat q gained or lost by an object is the product of its mass m, its specific heat c, and its change in temperature ΔT: q = mcΔT, where specific heat is the amount of heat required to increase a unit mass of a substance by 1°C (or 1 K).

A 100-G Block of Iron at 31°C Is Submerged in 50