Question

calculate the energy required to heat 0.80 kg of cyclohexane from 15.8 °c to 20.9 °c. assume the specific heat capacity of cyclohexane under these conditions is 1.85 j·g⁻¹·k⁻¹. be sure your answer has the correct number of significant digits.

Explanation:

Step1: Convert mass to grams

Since \(1\ kg = 1000\ g\), for \(m = 0.80\ kg\), we have \(m=0.80\times1000\ g = 800\ g\).

Step2: Calculate the temperature change

The formula for temperature change \(\Delta T=T_{final}-T_{initial}\). Given \(T_{initial}=15.8^{\circ}C\) and \(T_{final}=20.9^{\circ}C\), then \(\Delta T=(20.9 - 15.8)K=5.1K\) (since \(\Delta T\) in \(^{\circ}C\) is equal to \(\Delta T\) in \(K\)).

Step3: Use the heat - formula \(Q = mc\Delta T\)

The specific heat capacity \(c = 1.85\ J\cdot g^{-1}\cdot K^{-1}\), \(m = 800\ g\), \(\Delta T=5.1K\). Substitute into the formula: \(Q=(800\ g)\times(1.85\ J\cdot g^{-1}\cdot K^{-1})\times(5.1K)\).
First, calculate \(800\times1.85 = 1480\), then \(1480\times5.1=7548\ J\).

Answer:

\(7.5\times 10^{3}\ J\)