Question

question #4
ethanol, a liquid at room temperature, is the intoxicating component of alcoholic drinks. it has a specific heat of 0.578 (\frac{\text{cal}}{\text{g}cdot^circ\text{c}}). this means that it would require 0.578 cal of energy to raise the temperature of 1 g of ethanol by 1 (^circ)c.
what is the specific heat of ethanol in (\frac{\text{j}}{\text{g}cdot^circ\text{c}})?

Explanation:

Step1: Recall the conversion factor between calories and joules

We know that \( 1 \, \text{cal} = 4.184 \, \text{J} \).

Step2: Convert the specific heat from \(\frac{\text{cal}}{\text{g}^\circ\text{C}}\) to \(\frac{\text{J}}{\text{g}^\circ\text{C}}\)

Given the specific heat of ethanol is \( 0.578 \, \frac{\text{cal}}{\text{g}^\circ\text{C}} \). To convert this to joules per gram per degree Celsius, we multiply by the conversion factor \( 4.184 \, \frac{\text{J}}{\text{cal}} \).
So, \( 0.578 \, \frac{\text{cal}}{\text{g}^\circ\text{C}} \times 4.184 \, \frac{\text{J}}{\text{cal}} \)
First, multiply the numerical values: \( 0.578 \times 4.184 \approx 2.418 \)
The units cancel out the calories, leaving \( \frac{\text{J}}{\text{g}^\circ\text{C}} \).

Answer:

\( 2.42 \) (rounded to two decimal places, or more precisely \( 2.418 \)) \(\frac{\text{J}}{\text{g}^\circ\text{C}}\)