COMEDK2025PhysicsThermodynamicsActual
A given volume of gas at NTP is allowed to expand 6 times of its original volume, first under isothermal condition and then under adiabatic condition. Which of the given statement is correct? [Given C_p C_v = =1.4 ]
Options
- AThe final pressure after the adiabatic expansion is less than the final pressure after the isothermal expansio
- BPressure remains same in both adiabatic and isothermal expansion
- CThe final temperature after the adiabatic expansion is 1.4 times less than the final temperature after the iso
- DThe final pressure after the adiabatic expansion is 1.4 times greater than the final pressure after the isothe
Correct answer
A. The final pressure after the adiabatic expansion is less than the final pressure after the isothermal expansio
Step-by-step solution
Let the initial pressure be P₀ , initial volume be V₀ , and initial temperature be T₀ . The gas expands to a final volume V_f = 6V₀ . For isothermal expansion, the final pressure P_ iso is given by P₀ V₀ = P_ iso (6V₀) , which gives P_ iso = P₀ 6 . For adiabatic expansion, the final pressure P_ adia is given by P₀ V₀^ = P_ adia (6V₀)^ , which gives P_ adia = P₀ ( 1 6 )^ . Given = 1.4 , we have P_ adia = P₀ ( 1 6 )^ 1.4 . Comparing P_ iso = P₀ (6)⁻¹ and P_ adia = P₀ (6)^ -1.4 , since 6^ 1.4 > 6^1 , it follows that 1