To raise the temperature of a 2.0-kg piece of metal from 20ºC to 100ºC, 61.8 kJ of heat is added. What is the specific heat of this metal in kJ/(kg.K)?
Question 1 options:
A) 0.39
B) 0.31
C) 1.6
D) 1.2
E) 0.77
Familiarize yourself with the definition of specific heat:
C = (heat added)/[(mass)*(temp. rise)]
In this case, that would be
61.8/[(2*80)]
Do the calculation and make your selection.
Thank you
To find the specific heat of the metal, we can use the equation:
Q = m * c * ΔT
where Q is the heat added, m is the mass of the metal, c is the specific heat, and ΔT is the change in temperature.
Given:
Q = 61.8 kJ
m = 2.0 kg
ΔT = (100ºC - 20ºC) = 80ºC
Let's substitute these values into the equation and solve for c:
61.8 kJ = 2.0 kg * c * 80ºC
Rearranging the equation to solve for c:
c = 61.8 kJ / (2.0 kg * 80ºC)
Now, let's calculate the value of c:
c = 61.8 kJ / (2.0 kg * 80ºC)
c = 0.3875 kJ/(kg.K)
Therefore, the specific heat of the metal is approximately 0.39 kJ/(kg.K).
So, the correct answer is A) 0.39.
To find the specific heat of the metal, we need to use the formula:
Q = m * c * ∆T
Where:
Q is the amount of heat added (given as 61.8 kJ),
m is the mass of the metal (given as 2.0 kg),
c is the specific heat of the metal (what we want to find),
∆T is the change in temperature (100ºC - 20ºC = 80ºC).
Now, we can rearrange the formula to solve for c:
c = Q / (m * ∆T)
c = 61.8 kJ / (2.0 kg * 80ºC)
c = 0.773 kJ / (kgºC) (rounded to three decimal places)
So, the specific heat of the metal is approximately 0.773 kJ/(kgºC).
Comparing this value to the answer choices provided, we can see that the correct option is:
E) 0.77