The specific heat of ethylene glycol is 2.42 J/g-K.
How many J of heat are needed to raise the temperature of 62.0 g of ethylene glycol from 13.1 degrees celsius to 40.5 degrees celsius?
The correct answer and explanation is :
To calculate the heat required to raise the temperature of ethylene glycol, we use the heat equation:
[
q = mc\Delta T
]
where:
- ( q ) = heat energy (J)
- ( m ) = mass of the substance (g)
- ( c ) = specific heat capacity (J/g·K)
- ( \Delta T ) = change in temperature (°C or K)
Step 1: Identify Given Values
- ( m = 62.0 ) g
- ( c = 2.42 ) J/g·K
- Initial temperature ( T_i = 13.1 )°C
- Final temperature ( T_f = 40.5 )°C
Step 2: Calculate Temperature Change
[
\Delta T = T_f – T_i = 40.5 – 13.1 = 27.4 \text{°C}
]
Since the Celsius and Kelvin scales have the same interval size, we can use °C directly in the equation.
Step 3: Calculate Heat Energy
[
q = (62.0 \text{ g}) \times (2.42 \text{ J/g·K}) \times (27.4 \text{ K})
]
[
q = 4107.5 \text{ J}
]
Step 4: Round to Significant Figures
Since the given values have three significant figures, we round the final answer to three significant figures:
[
q = 4110 \text{ J}
]
Explanation
The specific heat capacity of a substance indicates how much heat energy is needed to raise the temperature of 1 gram of that substance by 1 K (or 1 °C). Ethylene glycol has a specific heat of 2.42 J/g·K, meaning it requires 2.42 joules of energy to raise the temperature of 1 gram of ethylene glycol by 1°C.
In this case, 62.0 g of ethylene glycol undergoes a temperature increase of 27.4°C. Since energy is proportional to mass and temperature change, we use the formula ( q = mc\Delta T ) to determine that 4110 J of heat energy is needed.
This calculation is useful in real-life applications like engine coolants, where ethylene glycol is commonly used due to its high specific heat, helping regulate engine temperature efficiently.