Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Concepts Of Physics MCQ Edition [Volume 2]PhysicsSpecific Heat Capacities of Gases

An adiabatic cylindrical tube having a volume V₀ is separated into two parts by a frictionless adiabatic separator, as shown in the figure. Initially, the separator is held in the middle. The left part is filled with an ideal gas at pressure p₁ and temperature T₁ , while the right part contains another ideal gas at pressure p₂ and temperature T₂ . The specific heat ratio, C_p / C_V = , is identical for both gases. Th

Options

  1. Ap₁^ 1/ V₀ p₁^ 1/ + p₂^ 1/ and p₂^ 1/ V₀ p₁^ 1/ + p₂^ 1/
  2. Bp₂^ 1/ V₀ p₁^ 1/ + p₂^ 1/ and p₁^ 1/ V₀ p₁^ 1/ + p₂^ 1/
  3. Cp₁ V₀ p₁ + p₂ and p₂ V₀ p₁ + p₂
  4. Dp₁^ V₀ p₁^ + p₂^ and p₂^ V₀ p₁^ + p₂^

Correct answer

A. p₁^ 1/ V₀ p₁^ 1/ + p₂^ 1/ and p₂^ 1/ V₀ p₁^ 1/ + p₂^ 1/

Step-by-step solution

Since the separator is adiabatic and the process is slow, the expansion or compression of both gases is reversible and adiabatic. For an adiabatic process, pV^ = constant . Let the final pressure of both gases in equilibrium be p . The initial volume of each part is V₀ 2 . For the left part: p₁ ( V₀ 2 )^ = p V₁^ V₁ = V₀ 2 ( p₁ p )^ 1/ For the right part: p₂ ( V₀ 2 )^ = p V₂^ V₂ = V₀ 2 ( p₂ p )^ 1/ The total volume of the tube remains constant, so V₁ + V₂ = V₀ . Substituting the expressions for V₁ and V₂ : V₀ 2 ( p₁

Practice Specific Heat Capacities of Gases on Quantrex Academy →

More from Specific Heat Capacities of Gases

The ratio of molar heat capacities for an ideal gas is given as C_p / C_V = 7/6 . Find the change in internal energy of 1.0 mole of the gas when its temperature is raised by 50 K aAn ideal gas has a molar heat capacity ratio of C_p / C_V = 7/6 . Determine the change in internal energy of 1.0 mole of this gas when its temperature is raised by 50 K while keepiAs illustrated in the figure, a cylindrical container holds oxygen ( = 1.4 ) and is sealed by a 50 kg frictionless piston. The cross-sectional area is 100 cm ^2 , the atmospheric pA vessel containing one mole of a monatomic ideal gas (molecular weight = 20 g mol ⁻¹ ) travels on a floor at a speed of 50 m s ⁻¹ . The vessel is abruptly brought to rest. AssuminWhen 50 J of heat is supplied to an ideal gas, it expands from 100 cm ^3 to 200 cm ^3 at a constant pressure of 2.0 10^5 Pa . Calculate the change in internal energy of the gas.An ideal gas expands from 100 cm ^3 to 200 cm ^3 at a constant pressure of 2.0 10^5 Pa when 50 J of heat is supplied to it. Assuming the initial temperature is 300 K , calculate thAn ideal gas expands from 100 cm ^3 to 200 cm ^3 at a constant pressure of 2.0 10^5 Pa upon being supplied with 50 J of heat. Determine the number of moles in the gas if its initiaDuring a particular process, a monatomic ideal gas absorbs an amount of heat Q and performs work equal to Q/2 on its surroundings. Determine the molar heat capacity of the gas for Full Specific Heat Capacities of Gases list All Concepts Of Physics MCQ Edition [Volume 2] PYQs