Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced2015PhysicsThermodynamicsActual

An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure).Initially the gas is at temperature T 1 , pressure P 1 and volume V 1 and the spring is in its relaxed state. The gas is then heated very slowly to temperature T 2 , pressure P 2 and volume V 2 . During this process the piston moves out by a distance x . Ignoring the friction between the piston the cylinder

Options

  1. AIf V 2 = 2 V 1 and T 2 = 3 T 1 , then the energy stored in the spring is 1 4 P 1 V 1
  2. BIf V 2 = 2 V 1 and T 2 = 3 T 1 , then the change in internal energy is 3 P 1 V 1
  3. CIf V 2 = 3 V 1 and T 2 = 4 T 1 , then the work done by the gas is 7 3 P 1 V 1
  4. DIf V 2 = 3 V 1 and T 2 = 4 T 1 , then the heat supplied to the gas is 17 6 P 1 V 1

Correct answer

A. If V 2 = 2 V 1 and T 2 = 3 T 1 , then the energy stored in the spring is 1 4 P 1 V 1

Step-by-step solution

(i) P = P 1 + K x A P 2 = 3 2 P 1 ⇒ x = V 1 A 3 P 1 2 = P 1 + K x A K x = P 1 A 2 Energy of spring 1 2 K x 2 = P 1 A 4 x = P 1 V 1 4 (ii) ∆ U = f 2 P 2 V 2 - P 2 V 1 = 3 P 1 V 1 (iii) P f = 4 P 1 3 K X = P 1 3 A X = 2 V 1 A W g a s = - W P a t m + W s p r i n g = P 1 A x + 1 2 K x . x = + P 1 A . 2 V 1 A + 1 2 . P 1 A 3 . 2 V 1 A = 2 P 1 V 1 + P 1 V 1 3 = 7 P 1 V 1 3 (iv) ∆ Q = W + ∆ U = 7 P 1 V 1 3 + 3 2 P 2 V 2 - P 1 V 1 = 7 P 1 V 1 3 + 3 2 4 3 P 1 . 3 V 1 - P 1 V 1 = 7 P 1 V 1 3 + 9 2 P 1 V 1 = 41 P 1 V 1 6

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