Question

How much heat is required to warm 1.50 L of water from \(25.0 ^ { \circ } \mathrm { C }\) to \(100.0 ^ { \circ } \mathrm { C } ?\) (Assume a density of 1.0\(\mathrm { g } / \mathrm { mL }\) . for the water.)

Short answer

The heat required is 6.27 × 10^5 Joules.

Step-by-step solution

Convert volume to mass

Firstly, convert the volume of water to mass since the specific heat capacity equation requires the mass of the substance. The density of water is given as 1.0 g/mL. To find the mass (m), use the formula: mass = density × volume. For water, 1.50 L (or 1500 mL) has a mass of 1500 g (since 1 mL of water has a mass of 1 g).

Calculate heat using specific heat capacity

Use the specific heat capacity equation Q = mcΔT to calculate the heat. Here, Q is the heat absorbed, m is the mass of water, c is the specific heat capacity of water (4.18 J/g°C), and ΔT is the change in temperature. Since the water needs to be heated from 25.0°C to 100.0°C, ΔT = 100.0°C - 25.0°C = 75.0°C.

Perform the calculation

Substitute the values into the equation: Q = mcΔT Q = (1500 g)(4.18 J/g°C)(75.0°C) Q = 6.27 × 10^5 J The heat required is 6.27 × 10^5 Joules.

Key concepts

Specific Heat Capacity

Understanding the specific heat capacity is essential when calculating the amount of heat needed to change the temperature of a substance. Specific heat capacity, symbolized as 'c', is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius (or one Kelvin). Different substances have different capacities for storing heat, meaning that they require varying amounts of energy to achieve the same temperature change. For instance, water has a relatively high specific heat capacity at roughly 4.18 Joules per gram per degree Celsius (\(4.18 \frac{J}{g^{\bullet}C}\)). This explains why water is used in many cooling and heating applications, as it can absorb or release a significant amount of heat with little change in temperature.

When solving problems that involve heat calculations, you need to multiply the specific heat capacity by the mass of the substance and the change in temperature. This product gives you the quantity of heat absorbed or released. It's worth noting that the specific heat capacity is usually measured at a constant pressure, often abbreviated to 'cp'.

Temperature Conversion

Temperature conversion is a fundamental process in understanding heat calculations in chemistry. Since temperature can be measured in different scales, Celsius (\(^\bullet C\)), Fahrenheit (\(^\bullet F\)), and Kelvin (\(K\)), it's often necessary to convert between these units to accurately calculate heat energy transfer. The Celsius and Kelvin scales are the most commonly used in scientific contexts, with a directly proportional relationship where a change of 1 degree Celsius is equivalent to a change of 1 Kelvin.

The formula for converting from Celsius to Kelvin is simply: \[ K = C + 273.15 \] It's important to remember that Kelvin does not include a degree sign (\(^\bullet\)) because it is an absolute temperature scale, starting from absolute zero (0 K), the theoretical lowest possible temperature. Using Kelvin is particularly useful in theoretical and experimental chemistry where equations often call for absolute temperatures.

Energy Transfer in Thermal Processes

Energy transfer in thermal processes is a key concept that explains how heat moves from one body to another or transforms within a system. Heat is a form of energy, and in physics, energy transfer is classified into work and heat transfer. For the purposes of our chemistry exercise, we're looking at heat transfer, which is fundamentally the movement of thermal energy due to a temperature difference. In this context, 'heat' is measured in energy units such as Joules (\(J\)).

There are three modes of heat transfer: conduction, convection, and radiation. In a heating scenario, such as warming water, energy is transferred to the water molecules, increasing their kinetic energy and thus the temperature of the water. The heat calculation formula, \[ Q = mc\Delta T \] where \(Q\) is the heat energy transferred, \(m\) is the mass, \(c\) the specific heat capacity, and \(\Delta T\) the change in temperature, illustrates how energy is needed to increase the substance's temperature. Knowing how heat transfer operates is crucial for solving problems involving thermal processes and is widely applicable in various fields of science and engineering.