Q.Define two specific heat capacities of a gas and derive the relation between them on the basis of first law of thermodynamics.

Showing the 12 most recent of 15 on this concept.

1. CBSE 2026Set ANNUAL1 markMCQ
   Q.The ratio of Molar specific Heats (Cp/Cv) of Monoatomic gas is :

   (a) 5/3

   (b) 5/7

   (c) 7/9

   (d) 7/5.

   ›Reveal solutionSolution

   A monoatomic gas has 3 degrees of freedom, giving Cv = (3/2)R, Cp = (5/2)R, and hence Cp/Cv = 5/3.

   By the law of equipartition of energy, each degree of freedom contributes (1/2)RT to the internal energy per mole of an ideal gas.

   A monoatomic gas (e.g. He, Ar) has only 3 translational degrees of freedom (no rotational or vibrational contribution for a point-like molecule at ordinary temperatures).

   …

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2. CBSE 2026Set ANNUAL1 markMCQ
   Q.The ratio of Cp and Cv for helium gas is

   (a) 5/3

   (b) 5/7

   (c) 3/5

   (d) 9/7

   ›Reveal solutionSolution

   Helium is monatomic, so gamma = Cp/Cv = 5/3. Answer (A).

   For a monatomic ideal gas (3 translational degrees of freedom):

   Cv = (3/2)R and Cp = Cv + R = (5/2)R.

   …

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3. CBSE 2025Set ANNUAL1 markMCQ
   Q.Mayer's formula is (A) C_P - C_V = R (B) C_P/C_V = R (C) C_V - C_P = R (D) C_V/C_P = R

   ›Reveal solutionSolution

   Mayer's formula states $C_P - C_V = R$ for one mole of an ideal gas.

   At constant volume, all the heat supplied goes into raising internal energy: $dQ = C_VdT = dU$.

   At constant pressure, the gas also does work as it expands, so extra heat is needed for the same temperature rise: $dQ = C_PdT = dU + PdV$.

   For 1 mole of an ideal gas, $PV=RT \Rightarrow PdV = RdT$ at constant pressure. Substituting:

   …

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4. CBSE 2025Set ANNUAL1 mark
   Q.Answer in one word or one sentence: Write Mayer's equation.

   ›Reveal solutionSolution

   Mayer's relation states Cp - Cv = R for an ideal gas.

   For one mole of an ideal gas, the molar specific heat at constant pressure (Cp) exceeds the molar specific heat at constant volume (Cv), because at constant pressure some of the supplied heat must also do work as the gas expands, in addition to raising its internal energy. Using the first law of thermodynamics and the ideal gas e …

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5. CBSE 2024Set ANNUAL1 markMCQ
   Q.The ratio of specific heats (γ) of diatomic gas is:

   (a) 3/5

   (b) 5/7

   (c) 7/9

   (d) 7/5

   ›Reveal solutionSolution

   Using the equipartition theorem, a diatomic gas has 5 degrees of freedom, giving Cv = 5R/2, Cp = 7R/2, and hence gamma = Cp/Cv = 7/5.

   For an ideal gas molecule with f degrees of freedom, the equipartition theorem gives the molar internal energy as U = (f/2)RT, so:

   Cv = dU/dT = (f/2)R

   Cp = Cv + R = (f/2)R + R = [(f+2)/2]R

   gamma = Cp/Cv = (f+2)/f

   …

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6. CBSE 2024Set ANNUAL1 markMCQ
   Q.The total internal energy of a mono atomic gas is

   (a) a) (1/2)KBT

   (b) b) (1/3)KBT

   (c) c) (3/2)KBT

   (d) d) (5/2)KBT

   ›Reveal solutionSolution

   [!TLDR]

   c) (3/2)KBT

   Why

   A monatomic gas molecule has 3 translational degrees of freedom; by the law of equipartition of energy, average energy …

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7. CBSE 2023Set ANNUAL1 markMCQ
   Q.Mayer's formula for the relation between two principal specific heats Cp and Cv of a gas is given by

   (1) Cv - Cp = R

   (2) Cp / Cv = R

   (3) Cp - Cv = R

   (4) Cv / Cp = R

   ›Reveal solutionSolution

   For one mole of an ideal gas, Mayer's relation states Cp - Cv = R, where R is the universal gas constant.

   For an ideal gas, heating it at constant volume only increases its internal energy (all the heat goes into raising temperature), while heating it at constant pressure must also supply energy for the gas to do work as it expands (W = PΔV = RΔT for one mole). This extra work requirement is exactly what makes Cp larger than Cv, and the difference between them equals the gas constant R per mole:

   Cp - Cv = R

   …

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8. CBSE 2022Set ANNUAL1 markMCQ
   Q.In the relation PV^γ = constant, γ is:

   (a) Cp - Cv

   (b) Cp / Cv

   (c) Cp . Cv

   (d) Cp + Cv

   ›Reveal solutionSolution

   The symbol γ in the adiabatic relation PV^γ = constant is the ratio of specific heat at constant pressure to specific heat at constant volume, γ = Cp/Cv.

   For a reversible adiabatic process on an ideal gas, combining the first law of thermodynamics (dQ = 0) with the ideal gas equation PV = nRT gives PV^γ = constant, where γ = Cp/Cv. This ratio is always greater than 1 because Cp > Cv (at constant pressure, some of the added heat goes int …

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9. CBSE 2022Set ANNUAL1 markMCQ
   Q.Match Column A item "Mayer's relation" with the correct item in Column B.

   (a) kg m^2

   (b) Poise

   (c) Cp - Cv = R

   (d) E = mc^2

   (e) 1/frequency

   (f) distance

   (g) 24 hours

   ›Reveal solutionSolution

   Mayer's relation states Cp - Cv = R (per mole), showing that the extra heat needed at constant pressure over constant volume goes entirely into the work of expansion.

   …

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10. CBSE 2022Set ANNUAL1 markMCQ
    Q.(Cp − Cv) is equal to —

    (a) R x J

    (b) R − J

    (c) R/J

    (d) J/R

    ›Reveal solutionSolution

    Cp − Cv = R/J (molar heat capacities in calorie/heat units).

    Mayer's relation for one mole of an ideal gas, when the heat capacities are in energy (joule) units, is $C_p - C_v = R$.

    …

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11. CBSE 2020Set ANNUAL1 markMCQ
    Q.The molar specific heat at constant pressure of an ideal gas is (7/2) R. The ratio of specific heat at constant pressure to that at constant volume is:

    (a) 9/7

    (b) 7/5

    (c) 8/7

    (d) 5/7

    ›Reveal solutionSolution

    Mayer's relation connects Cp and Cv for an ideal gas (Cp - Cv = R); once Cv is found, the ratio gamma = Cp/Cv follows directly.

    Given Cp = (7/2) R.

    Mayer's relation: Cp - Cv = R, so Cv = Cp - R = (7/2) R - R = (5/2) R.

    gamma = Cp / Cv = [(7/2) R] / [(5/2) R] = 7/5.

    …

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12. CBSE 2020Set ANNUAL1 markMCQ
    Q.The kinetic energy of one mole of an ideal gas is E = 3/2 RT. The value of Cp is:

    (a) 0.5 R

    (b) 0.1 R

    (c) 1.5 R

    (d) 2.5 R

    ›Reveal solutionSolution

    The given internal (kinetic) energy expression identifies Cv = (3/2)R directly; adding R (Mayer's relation) gives Cp = (5/2)R = 2.5R.

    For one mole of an ideal gas, internal energy (here treated as the total kinetic energy) is E = (3/2) R T, which by definition means:

    Cv = dE/dT = (3/2) R.

    …

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