Question

Four kg of water is placed in an enclosed volume of 1m3. Heat is added until the temperature is 150°C. Find ( a ) the pressure, ( b )the mass of vapor, and ( c ) the volume of the vapor.

Answer 1

Answer on Question #66214, Physics / Solid State Physics

Four kg of water is placed in an enclosed volume of 1m³. Heat is added until the temperature is 150°C. Find (a) the pressure, (b) the mass of vapor, and (c) the volume of the vapor.

Solution:

a) We use the table of Saturated water—Temperature. In the quality region the pressure is given as p = 476.16 kPa

b) To find the mass of the vapor we must determine the quality. We use the next equation:

$$v = v_f + x(v_g - v_f)$$

Then,

$$\begin{array}{l} 0.25 \, \mathrm{m}^3/\mathrm{kg} = 0.001091 \, \mathrm{m}^3/\mathrm{kg} + x(0.39248 - 0.001091) \, \mathrm{m}^3/\mathrm{kg} \\ 0.25 = 0.001091 + 0.391389x \\ 0.391389x = 0.25 - 0.001091 \\ 0.391389x = 0.248909 \\ x = 0.248909 \, (\mathrm{m}^3/\mathrm{kg}) / 0.391389 \, (\mathrm{m}^3/\mathrm{kg}) \\ x = 0.63596 \\ \end{array}$$

Using the relationship of $x = \frac{m_g}{m}$, we find the vapor mass

$$m_g = x m = 0.63596 \times 4 \, \mathrm{kg} = 2.544 \, \mathrm{kg}$$

c) The volume of the vapor is found from

$$V_g = v_g m_g = 2.544 \, \mathrm{kg} \times 0.39248 \, \mathrm{m}^3/\mathrm{kg} = 0.998 \, \mathrm{m}^3$$

Answer: 476.16 kPa; 2.544 kg; 0.998 m³

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