Explanation Given: Temperature of line is 540 R . Pressure of line is 75 lbf/in 2 . Volume of tank is 2000 ft 3 . Pressure of tank is 75 lbf/in 2 . The final temperature is 450 R . Concept used: Write the expression for energy balance for tank. m 2 u 2 − m 1 u 1 = m i n h i n + Q − W Here, m 2 is the final mass in tank, u 2 is the final internal energy of tank, m 1 is the initial mass in tank, u 1 is the initial internal energy of tank, m i n is the mass enter the tank, h i n is the enthalpy of Nitrogen inside the tank, Q is the heat transfer and W is the work done by turbine. Substitute 0 for m 1 and 0 for Q in above expression. m 2 u 2 − 0 u 1 = m i n h i n + 0 − W The mass enter inside the tank will be equal to the final mass of Nitrogen inside the tank. Substitute m 2 for m i n and simplify above expression. m 2 u 2 = m 2 h i n − W ..... (1) Write the expression for specific volume of nitrogen using ideal gas equation. v 2 = R T 2 p 2 ..... (2) Here, v 2 is the specific volume of Nitrogen corresponding to 75 lbf/in 2 , R is the gas constant for Nitrogen and T 2 is the final temperature of tank. Write the expression for final mass of Nitrogen in the tank. m 2 = V v 2 ..... (3) Here, V is the volume of tank. Substitute u i + R T i for h i in equation (1). m 2 u 2 = m 2 ( u i + R T i ) − W W = m 2 ( u i + R T − u 2 ) Substitute C v ( T i − T 2 ) for u i − u 2 and simplify above expression

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Chapter 4, Problem 4.132EP

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The point at which temperature is 250 K and turbine work.

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The point at which temperature is 250 K and turbine work.

Solution Summary: The author analyzes the energy balance of the tank. The mass enters it equal to the final mass of Nitrogen inside.

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