Suppose it is winter and the system is filled with methanol. The density of methanol is 0.80 g/cm3. What would be the increase in temperature of the methanol if it absorbed 836.0 kJ of heat
The Correct Answer and Explanation is:
Based on the data, the increase in temperature of the methanol would be 413.0 °C.
Explanation
The relationship between heat energy, mass, specific heat, and temperature change is described by the specific heat formula. This principle states that the amount of heat absorbed or released by a substance is directly proportional to its mass and the change in its temperature. The formula is expressed as:
Q = mcΔT
Where:
- Q is the heat energy absorbed or released (in Joules, J).
- m is the mass of the substance (in grams, g).
- c is the specific heat capacity of the substance (in J/g°C). This is a constant value unique to each material, representing the energy required to raise the temperature of 1 gram of the substance by 1 degree Celsius. For methanol, the value is approximately 2.53 J/g°C.
- ΔT (delta T) is the change in temperature (in °C), which we need to find.
Step 1: Determine the mass of the methanol.
The problem does not provide the mass directly but gives the density. To make the problem solvable, we must assume a standard volume, such as 1.0 liter (1000 cm³). Using the density, we can calculate the mass.
- Volume (V) = 1000 cm³
- Density (ρ) = 0.80 g/cm³
- Mass (m) = V × ρ = 1000 cm³ × 0.80 g/cm³ = 800 g
Step 2: Convert the heat energy to Joules.
The heat absorbed (Q) is given in kilojoules (kJ). We must convert it to Joules to match the units of the specific heat capacity.
- Q = 836.0 kJ × 1000 J/kJ = 836,000 J
Step 3: Calculate the temperature increase (ΔT).
Rearrange the specific heat formula to solve for ΔT:
ΔT = Q / (mc)
Now, substitute the known values into the equation:
ΔT = 836,000 J / (800 g × 2.53 J/g°C)
ΔT = 836,000 / 2024
ΔT = 413.0 °C
Therefore, the absorption of 836.0 kJ of heat would cause the temperature of 1.0 L of methanol to increase by 413.0 °C.thumb_upthumb_down
