Sure, let's solve the problem step-by-step.
1. Understanding the Problem:
- We need to find the heat required to raise the temperature of a certain mass of ethanol.
- The specific heat capacity of ethanol is given, which is the amount of heat required to raise the temperature of 1 gram of ethanol by 1°C.
- We are given the mass of ethanol and the change in temperature.
2. Given Data:
- Mass of ethanol, [tex]\( m = 193 \, \text{g} \)[/tex]
- Specific heat capacity of ethanol, [tex]\( c = 2.46 \, \text{J/g}^\circ\text{C} \)[/tex]
- Initial temperature, [tex]\( T_i = 19^\circ\text{C} \)[/tex]
- Final temperature, [tex]\( T_f = 35^\circ\text{C} \)[/tex]
3. Change in Temperature:
- Calculate the change in temperature, [tex]\( \Delta T \)[/tex]:
[tex]\[
\Delta T = T_f - T_i = 35^\circ\text{C} - 19^\circ\text{C} = 16^\circ\text{C}
\][/tex]
4. Formula for Heat Required:
- The formula for the heat required to change the temperature of a substance is:
[tex]\[
Q = mc\Delta T
\][/tex]
where [tex]\( Q \)[/tex] is the heat required, [tex]\( m \)[/tex] is the mass, [tex]\( c \)[/tex] is the specific heat capacity, and [tex]\( \Delta T \)[/tex] is the change in temperature.
5. Substitute the Values:
- Substitute the given values into the formula:
[tex]\[
Q = 193 \, \text{g} \times 2.46 \, \text{J/g}^\circ\text{C} \times 16^\circ\text{C}
\][/tex]
6. Calculate the Heat Required:
- Perform the multiplication:
[tex]\[
Q = 193 \times 2.46 \times 16 = 7596.48 \, \text{J}
\][/tex]
Therefore, the heat required to raise the temperature of 193 grams of ethanol from [tex]\(19^\circ\text{C}\)[/tex] to [tex]\(35^\circ\text{C}\)[/tex] is [tex]\(7596.48\)[/tex] Joules.
