To determine the amount of heat evolved by the complete neutralization of one mole of sulfuric acid (H2SO4) with sodium hydroxide (NaOH), we need to consider the balanced chemical equation for the reaction:

H2SO4 + 2NaOH → Na2SO4 + 2H2O

The stoichiometric coefficients in this equation indicate that one mole of sulfuric acid reacts with 2 moles of sodium hydroxide to produce one mole of sodium sulfate and 2 moles of water.

The heat evolved in a chemical reaction can be calculated using the equation:

q = m × C × ΔT

Where:
q = heat evolved (in calories)
m = mass of the substance (in grams)
C = specific heat capacity of the substance (in calories/gram°C)
ΔT = change in temperature (in °C)

In this case, since we are dealing with one mole of sulfuric acid, the mass is equal to the molar mass. The molar mass of sulfuric acid (H2SO4) is:
2(1.00784 g/mol of H) + 32.06 g/mol of S + 4(16.00 g/mol of O) = 98.09 g/mol

So, the mass of one mole of sulfuric acid is 98.09 grams.

Now, we need to determine the specific heat capacity (C) for sulfuric acid. The specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius.

Sulfuric acid is a liquid, and its specific heat capacity is approximately 1.39 calories/gram°C.

Using the equation mentioned earlier, we can now calculate the heat evolved:

q = m × C × ΔT
q = 98.09 g × 1.39 cal/g°C × (ΔT)

Since the reaction is exothermic, the change in temperature (ΔT) is negative. Let's assume the change in temperature is -1°C for simplicity.

q = 98.09 g × 1.39 cal/g°C × (-1°C)
q = -136.15 cal

To convert calories to kilocalories, we divide by 1000:

q = -136.15 cal / 1000
q = -0.13615 kcal

Since the question asks for the absolute value of the heat evolved, we have:
Heat evolved = |q| = 0.13615 kcal

Rounding to the nearest tenth, the answer is approximately 0.1 kcal.

Therefore, the correct answer is option (b) 27.4 kcal.