Water at room temperature, 20°C, is pumped into a reactor core where it is converted to steam at 200°C. How much heat (in J) is transferred to each kilogram of water in this process? (csteam = 2 010 J/kg⋅°C; LV,steam = 2.26 × 10³ J/g; 1 cal = 4.186 J.)

Question

Quizplus · Accepted Answer

To find the heat transferred to each kilogram of water, we need to use the formula:

Q = m * (h2 - h1)

where Q is the heat transferred, m is the mass of water, h2 is the enthalpy of steam at 200°C, and h1 is the enthalpy of water at 20°C.

First, let's convert LV,steam to J/kg:

LV,steam = 2.26 × 10^6 J/kg

Now, we need to find the enthalpy values. We can use tables to look up these values, or we can use the following equations:

h1 = cp,water * (T2 - T1)
h2 = cp,steam * (T2 - T1) + LV,steam

where cp,water is the specific heat of water, cp,steam is the specific heat of steam, and T1 and T2 are the initial and final temperatures.

Using these equations and the given values, we get:

h1 = (4.186 J/g°C * 1000 g/kg) * (200 - 20) = 314,760 J/kg
h2 = (2,010 J/kg°C * 1000 g/kg) * (200 - 20) + 2.26 × 10^6 J/kg = 2,926,000 J/kg

Now we can plug these values into the formula:

Q = m * (h2 - h1) = 1 kg * (2,926,000 J/kg - 314,760 J/kg) = 2.81 × 10^6 J/kg

Finally, we need to convert this answer from J/kg to x10^15 J/kg:

2.81 × 10^6 J/kg = 2.81 × 10^-15 x10^15 J/kg = 2.81 x 10^15 J/kg = 2.80 × 10^16 J/kg

Therefore, the answer is D.

Water at Room Temperature, 20°C, Is Pumped into a Reactor