Understanding the concept of specific heat capacity is crucial in thermodynamics. This problem involves calculating the specific heat of a fluid when heat energy is supplied to it, causing a temperature rise at constant pressure. We will use the fundamental formula relating heat energy, mass, specific heat, and temperature change to find the average specific heat of the fluid.

Fluid Specific Heat Calculation

The heat energy supplied to a substance, its mass, its specific heat capacity, and the resulting change in temperature are related by a simple formula. This formula helps us quantify how much energy is needed to change the temperature of a given mass of a substance.

The relevant formula for heat transfer is:

\(\Delta Q = m \times C \times \Delta T\)

Where:

• \(\Delta Q\) is the heat energy supplied (in Joules, J).
• \(m\) is the mass of the fluid (in kilograms, kg).
• \(C\) is the specific heat capacity of the fluid (in J/kg°C).
• \(\Delta T\) is the change in temperature (in degrees Celsius, °C).

Since the heat is supplied at constant pressure, the specific heat capacity we are looking for is the specific heat at constant pressure, denoted as \(C_p\).

Given Values

From the question, we are provided with the following values:

• Heat energy supplied, \(\Delta Q = 1800 \, \text{J}\)
• Mass of the fluid, \(m = 2 \, \text{kg}\)
• Rise in temperature, \(\Delta T = 15 \, \text{°C}\)

Step-by-Step Calculation of Specific Heat

To find the average specific heat of the fluid, \(C_p\), we can rearrange the heat transfer formula:

\(C_p = \frac{\Delta Q}{m \times \Delta T}\)

Now, substitute the given numerical values into the rearranged formula:

\(C_p = \frac{1800 \, \text{J}}{2 \, \text{kg} \times 15 \, \text{°C}}\)

Perform the multiplication in the denominator first:

\(C_p = \frac{1800 \, \text{J}}{30 \, \text{kg°C}}\)

Finally, perform the division:

\(C_p = 60 \, \text{J/kg°C}\)

Specific Heat Result Analysis

The calculated average specific heat of the fluid at constant pressure is \(60 \, \text{J/kg°C}\). This value represents the amount of heat energy required to raise the temperature of one kilogram of the fluid by one degree Celsius at constant pressure.

Comparing with Options

Let's compare our calculated specific heat value with the given options:

Our calculated value \(C_p = 60 \, \text{J/kg°C}\) matches Option 2 perfectly.

Key Concepts Revisited

• Specific Heat Capacity (\(C\)): This is a physical property of matter, defined as the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius (or Kelvin).
• Constant Pressure (\(C_p\)): When heat transfer occurs at constant pressure, the specific heat capacity is denoted as \(C_p\). This is relevant for processes occurring in open containers or systems where pressure is maintained.
• Constant Volume (\(C_v\)): If heat transfer occurs at constant volume, the specific heat capacity is denoted as \(C_v\). This is relevant for processes occurring in rigid, closed containers. For liquids and solids, \(C_p\) and \(C_v\) are very nearly the same, but for gases, they differ significantly. In this problem, the "constant pressure" condition clearly points to \(C_p\).

Therefore, the average specific heat of the fluid at constant pressure is \(60 \, \text{J/kg°C}\).