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, andΔT is the temperature increase (T₂ - T₁)
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.