Use the heat equation to calculate the energy, in joules and calories, for each of the following (see TABLE 3.11): c. lost when 15.0 g of ethanol, C₂H₆O, cools from 60.5 °C to −42.0 °C

Verified step by step guidance

1. Identify the specific heat capacity of ethanol from a reliable source, as the table provided only contains data for methanol.
2. Use the heat equation: q = m * c * ΔT, where q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
3. Calculate the change in temperature (ΔT) by subtracting the final temperature from the initial temperature: ΔT = -42.0 °C - 60.5 °C.
4. Substitute the values into the heat equation: m = 15.0 g, c = specific heat capacity of ethanol, and ΔT from the previous step.
5. Perform the calculation to find the energy lost in joules, then convert the result to calories using the conversion factor: 1 cal = 4.184 J.

Key Concepts

Heat Equation

The heat equation is a formula used to calculate the amount of heat energy absorbed or released by a substance when its temperature changes. It is expressed as Q = mcΔT, where Q is the heat energy (in joules or calories), m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature. Understanding this equation is crucial for solving problems related to thermal energy transfer.

Specific Heat Capacity

Specific heat capacity is a property of a substance that indicates the amount of heat required to change the temperature of one gram of the substance by one degree Celsius. It varies between different materials and is essential for calculating heat transfer in thermal processes. In this case, knowing the specific heat capacity of ethanol will allow for accurate energy calculations when it cools.

Energy Conversion (Joules to Calories)

Energy conversion between joules and calories is important for expressing thermal energy in different units. One calorie is equivalent to approximately 4.184 joules. When calculating energy changes, it may be necessary to convert between these units to meet specific requirements or preferences in reporting results. Understanding this conversion is vital for providing answers in both joules and calories.