The GATE Grind

GATE 2021 ME (ME1) – Question 22

Thermodynamics · Ideal and real gases · 1 mark · Multiple choice

Superheated steam at 1500 kPa, has a specific volume of 2.75 m³/kmol and compressibility factor ($Z$) of 0.95. The temperature of steam is _____ °C (round off to the nearest integer).

  1. 522
  2. 471
  3. 249
  4. 198

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Correct answer: (C) 249

Explanation

Use the real-gas relation $P\bar v=ZR_uT$ with $R_u=8.314$ kPa·m³/(kmol·K). Then $T=1500(2.75)/(0.95\times8.314)=522.27$ K.

Subtract 273.15 to obtain 249.12°C, rounded to **249°C (C)**. The volume is per kmol, so use the universal rather than mass-specific gas constant.