Question

An iron block of mass 18 kg is heated from 285 K to 318 K. If 267.3 kJ is required, what is the specific heat of iron? A. 450.00 B. 145.80 C. 158.77 D. 490.05

I am looking for an ABC or D not a long list of explanations

Answer 1

Answer:

• Option A. 450.00

Explanation:

1) Data:

a) m = 18 kg

b) T₁ = 285 K

c) T₂ = 318 K

d) Q = 267.3 kJ

e) S = ?

2) Principles and equations

The specific heat of a substance is the amount of heat energy absorbed to increase the temperature of certain amount (gram, kg, or moles, depending on the definition or units) of the substance in 1 ° C or 1 K.

The mathematical relation between the specific heat and the heat energy absorbed is:

• Q = m × S × ΔT

Where,

• Q is the heat absorbed,
• S is the specific heat, and
• ΔT is the temperature increase (T₂ - T₁)

3) Solution:

a) Substitute the data into the equation:

• 267.3 kJ = 18 kg × S × (318 K - 285 K)

b) Solve for S and compute:

• S = 267.3 kJ / (18 kg × 33 K) = 0.45 kJ / (Kg . K)

The options have not units, but I notice that the first answer is 1,000 times the answer I obtained, so I will make a conversion of units.

c) Convert to J /( kg . k):

• 0.45 kJ / (Kg . K) × 1,000 J / kJ = 450 J / (kg . K)

Now we can see that the option A is is the answer, assuming the units.