Questions: Calculate the energy required to heat 129.0 g of ethanol from 2.8°C to 20.3°C. Assume the specific heat capacity of ethanol under these conditions is 2.44 J · g^(-1) · K^(-1). Round your answer to 3 significant digits.

Solution Steps

We are given the following values:

• Mass of ethanol, \( m = 129.0 \, \text{g} \)
• Initial temperature, \( T_i = 2.8^{\circ} \text{C} \)
• Final temperature, \( T_f = 20.3^{\circ} \text{C} \)
• Specific heat capacity of ethanol, \( c = 2.44 \, \text{J} \cdot \text{g}^{-1} \cdot \text{K}^{-1} \)

The change in temperature, \(\Delta T\), is calculated as follows: \[ \Delta T = T_f - T_i = 20.3 - 2.8 = 17.5 \, \text{C} \]

Since the temperature change in Celsius is equivalent to the change in Kelvin, \(\Delta T = 17.5 \, \text{K}\).

The energy required, \( Q \), to heat the ethanol can be calculated using the formula: \[ Q = m \cdot c \cdot \Delta T \]

Substituting the given values: \[ Q = 129.0 \, \text{g} \times 2.44 \, \text{J} \cdot \text{g}^{-1} \cdot \text{K}^{-1} \times 17.5 \, \text{K} \]

Calculating the energy: \[ Q = 129.0 \times 2.44 \times 17.5 = 5500.62 \, \text{J} \]

Rounding to 3 significant digits, the energy required is: \[ Q = 5500 \, \text{J} \]

Final Answer