(d) How many kJ of heat are needed to raise the temperature of 10.00 kg of liquid water from 24.6 to 46.2 °C?

Verified step by step guidance

1. Identify the formula to calculate the heat required to change the temperature of a substance: \( q = mc\Delta T \), where \( q \) is the heat energy, \( m \) is the mass, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.
2. Determine the specific heat capacity of liquid water, which is typically \( 4.18 \text{ J/g°C} \).
3. Convert the mass of water from kilograms to grams, since the specific heat capacity is given in \( \text{J/g°C} \). For 10.00 kg, this is \( 10,000 \text{ g} \).
4. Calculate the change in temperature \( \Delta T \) by subtracting the initial temperature from the final temperature: \( 46.2°C - 24.6°C \).
5. Substitute the values into the formula: \( q = (10,000 \text{ g})(4.18 \text{ J/g°C})(\Delta T) \) and convert the result from joules to kilojoules by dividing by 1,000.

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. For water, this value is approximately 4.18 J/g°C. Understanding this concept is crucial for calculating the heat energy needed for temperature changes in substances.

Heat Transfer Equation

The heat transfer equation, often expressed as q = mcΔT, relates the heat energy (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 materials.

Units of Energy

Energy is commonly measured in joules (J) or kilojoules (kJ), where 1 kJ equals 1000 J. In thermodynamics, it is important to be consistent with units when performing calculations, especially when converting between different energy units to ensure accurate results.