KVPY2017PhysicsThermodynamics
A gas obeying the equation of state PV = RT undergoes a hypothetical reversible process described by the equation, PV ^ 5 / 3 (- PV E ₀ )= c ₁ where c₁ and E₀ are dimensioned constants. Then, for this process, the thermal compressibility at high temperature
Options
- Aapproaches a constant value.
- Bis proportional to T .
- Cis proportional to T ^ 1 / 2
- Dis proportional to T ² .
Correct answer
A. approaches a constant value.
Step-by-step solution
array l PV ^ 5 / 3 = c ₁ e ^ PV E ₀ P + 5 3 V = c ₁+ PV E ₀ dP P + 5 3 dV V =0+ PdV + VdP E ₀ dP [ 1 P - V E ₀ ]= d V [ P - 5 3 ~V ] c =- 1 ~V d V dP = [ 1 E ₀ - 1 PV ] [ P - 5 3 ~V ] array At very high temperature c= 1 E₀