Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced2020PhysicsThermodynamicsActual

Consider one mole of helium gas enclosed in a container at initial pressure P 1 and volume V 1 . It expands isothermally to volume 4 V 1 . After this, the gas expands adiabatically and its volume becomes 32 V 1 . The work done by the gas during isothermal and adiabatic expansion processes are W iso and W adia , W iso W adia = f ln 2 , then f is _________ .

Correct answer

0

Step-by-step solution

∴ γ = 5 3 In isothermal process, W 1 = n R T ln 4 V V = 2 n R T ln 2 In adiabatic process, T ( 4 V ) γ - 1 = T ' ( 32 V ) γ - 1 ⇒ T ' = T ( 8 ) 1 - γ = T × 8 - 2 3 = T 4 W 2 = - n 3 2 R T ' - T = + 3 2 nR 3 T 4 = 9 8 n R T W 1 W 2 = 2 n R T ln 2 9 8 n R T = 16 9 ln 2 = f ln 2 f = 16 9 = 1 . 78

Practice Thermodynamics on Quantrex Academy →

More from Thermodynamics

A quasi-static cycle of a monoatomic ideal gas contains an isothermal process ( ab ) , followed by an isochoric process ( bc ) and an adiabatic process ( ca ) as shown in the figur 2026As shown in the figure, five Carnot engines, each with efficiency and same number of cycles per unit time, are operating between six heat reservoirs. The amount of heat released pe 2026Ten moles of an ideal monoatomic gas, initially in state a at atmospheric pressure and temperature T_a = 27^ C, is enclosed in a metal cylinder of volume V₀ fitted with a frictionl 2026One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system. The cross-section area of the cylinder is 4 cm ^2 . The gas is heated slowly to ra 2026Initial pressure and volume of a monoatomic ideal gas are P and V . The change in internal energy of this gas in adiabatic expansion to volume V_ final =27V is ________ J. 2026A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the com 2026Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure 90 kPa and temperature 400 K. Keeping the temperature of one ves 2026A certain gas is isothermally compressed to ( 1 3 )^ rd of its initial volume ( V_o = 3 litre) by applying required pressure. If the bulk modulus of the gas is 3 10^5 N/m ^2 , the 2026 Full Thermodynamics list All JEE Advanced PYQs