The specific heat of ethanol, C₂H₅OH(l), is 2.44 J•g/K. (a) How many J of heat are needed to raise the temperature of 80.0 g of octane from 10.0 to 25.0 °C?

Verified step by step guidance

1. Identify the formula for calculating heat: \( q = m \cdot c \cdot \Delta T \), where \( q \) is the heat absorbed or released, \( m \) is the mass, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.
2. Note that the problem provides the specific heat of ethanol, but asks about octane. Ensure you have the correct specific heat for octane if needed.
3. Calculate the change in temperature \( \Delta T \) by subtracting the initial temperature from the final temperature: \( \Delta T = 25.0 \, ^\circ\text{C} - 10.0 \, ^\circ\text{C} \).
4. Substitute the given values into the formula: \( q = 80.0 \, \text{g} \times c \times \Delta T \).
5. Solve for \( q \) to find the amount of heat needed.

Key Concepts

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius (or Kelvin). It is a material-specific property that indicates how much energy is needed to change the temperature of a substance, which is crucial for calculations involving heat transfer.

Heat Transfer Equation

The heat transfer equation, often expressed as q = mcΔT, relates the heat (q) absorbed or released by a substance to its mass (m), specific heat capacity (c), and the change in temperature (ΔT). This equation is fundamental for solving problems involving temperature changes in substances, allowing for the calculation of heat energy based on the specific heat and mass.

Temperature Change

Temperature change (ΔT) is the difference between the final and initial temperatures of a substance. It is a critical component in the heat transfer equation, as it directly influences the amount of heat energy required to achieve a desired temperature change. Understanding how to calculate ΔT is essential for accurately determining heat transfer in chemical processes.