GATE XE (Engineering Sciences) 2024 - Question 67

Section: Thermodynamics | Marks: 1

Given 𝑣 is the molar specific volume, 𝑃 is the pressure, 𝑇 is the temperature, 𝑅 is the Universal gas constant, and 𝑎, 𝑏 are van der Waal’s constants. The van der Waal’s equation of state is 𝑃= 𝑅𝑇 𝑣−𝑏−𝑎 𝑣2 The value of ( 𝜕𝑣 𝜕𝑇) 𝑃( 𝜕𝑃 𝜕𝑣) 𝑇( 𝜕𝑇 𝜕𝑃) 𝑣 is

• A. 𝑎 𝑏2
• B. −1
• C. 1
• D. 𝑏2 𝑎

Answer: B. −1