Question

A 14.5 gram sample of solid iodine is at its melting point (113.7°C). How much energy is

Answer 1

The amount of energy required to raise the temperature of a 14.5 gram sample of solid iodine from its melting point (113.7°C) to its boiling point (184.3°C) can be calculated using the formula
`\(Q = mc\Delta T\)`, where
`\(Q\)` is the heat energy,
`\(m\)` is the mass,
`\(c\)` is the specific heat, and
`\(\Delta T\)` is the change in temperature. The specific heat of iodine is 0.214 J/g°C. The calculated energy required is approximately 444.92 joules.

Step-by-step explanation:

The heat energy
`(\(Q\))` required to change the temperature of a substance is given by the formula
`\(Q = mc\Delta T\)`, where
`\(m\)` is the mass,
`\(c\)` is the specific heat, and
`\(\Delta T\)` is the change in temperature. In this case, the sample of solid iodine is heated from its melting point (113.7°C) to its boiling point (184.3°C). The change in temperature is
`\(\Delta T = 184.3°C - 113.7°C = 70.6°C\)` . Given the mass
`\(m = 14.5 \, \text{g}\)` and the specific heat
`\(c = 0.214 \, \text{J/g°C}\)` for iodine, we can substitute these values into the formula to find
`\(Q\)`:

`\[Q = (14.5 \, \text{g})(0.214 \, \text{J/g°C})(70.6°C) \approx 444.92 \, \text{joules}\].`

The calculated energy represents the amount of heat required to raise the temperature of the solid iodine sample from its melting point to its boiling point. This process involves overcoming the heat of fusion to reach the melting point and then supplying additional energy to raise the temperature to the boiling point.

Understanding the heat transfer involved in changing the temperature of a substance is fundamental in thermodynamics. The specific heat, which characterizes the amount of heat needed to raise the temperature of a unit mass by one degree Celsius, is crucial in such calculations. The calculated energy value provides quantitative information about the heat requirements for the given temperature change in the solid iodine sample.