How much (in Celsius degrees) is the temperature of 1.3 kg of alcohol raised by adding 4.1 kcal of heat? The following piece of information may come in handy: specific heat of alcohol is 0.58 kcal/kgC.
I figured it out.
5.4377 was my final answer and that was right.
Excellent !
To find the change in temperature (ΔT) of a substance, we can use the formula:
ΔT = Q / (m × C)
where:
- ΔT is the change in temperature
- Q is the amount of heat added
- m is the mass of the substance
- C is the specific heat of the substance
In this case, we are given:
- Q = 4.1 kcal
- m = 1.3 kg
- C = 0.58 kcal/kg°C
Substituting the given values into the formula, the calculation becomes:
ΔT = 4.1 kcal / (1.3 kg × 0.58 kcal/kg°C)
First, let's simplify the units by converting 4.1 kcal to joules (J). Since 1 kcal = 4184 J, we have:
Q = 4.1 kcal × 4184 J/kcal = 17,104.4 J
Now we can continue the calculation:
ΔT = 17,104.4 J / (1.3 kg × 0.58 kcal/kg°C)
Next, simplify the units by converting the specific heat from kcal to J:
C = 0.58 kcal/kg°C × 4184 J/kcal = 2421.12 J/kg°C
Substituting the simplified values into the formula:
ΔT = 17,104.4 J / (1.3 kg × 2421.12 J/kg°C)
Now we can calculate ΔT:
ΔT = 17,104.4 J / (3,150.456 kg°C)
Finally, we get:
ΔT ≈ 5.429°C
Therefore, the temperature of 1.3 kg of alcohol is raised by approximately 5.429°C when 4.1 kcal of heat is added.