Specific Heats of Gases - Cp, Cv, γ & Mayer's Relation

The molar specific heat at constant pressure of an ideal gas is $\frac{7}{2}R$. The gas is made up of molecules which are

For a gas, if the ratio of specific heats at constant pressure and volume is $\gamma$ then the value of degree of freedom is

The ratio of $C_p$ to $C_v$ for a non-rigid diatomic gas is

According to law of equipartition of energy the molar specific heat of a non rigid diatomic gas at constant volume is

For a gas, $\frac{R}{C_v} = 0.4$ where R is the universal gas constant and $C_v$ is the molar specific heat at constant volume. The gas is made up of molecules which are

The difference between two molar specific heats of a gas is $7000$ J-kg$-1$-K $-1$. If the ratio of two specific heats of gas is $7/5$, the molar specific heat of the gas at constant pressure in J-kg $-1$-K $-1$ is

Let $\gamma_1$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a mono-atomic gas and $\gamma_2$ be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio, $\gamma_1/\gamma_2$ is

An ideal gas is made of polyatomic molecules. Each of the molecules has three translational, three rotational and $f$ number of vibrational modes. If the ratio of heat capacities $C_P/C_V$ of the gas is $8/7$, then the value of $f$ is:

For ideal non-rigid diatomic gas, the value of $\frac{R}{C_V}$ is nearly $\left(\gamma = \frac{C_P}{C_V} = \frac{9}{7}\right)$

The molar specific heat of an ideal gas at constant pressure and constant volume is ' $C_p$ ' and ' $C_v$ ' respectively. If ' R ' is a universal gas constant and the ratio of ' $C_p$ ' to ' $C_v$ ' is $\gamma$, then ' $C_p$ ' is equal to

For a diatomic gas, if $\gamma_1 = \left(\frac{C_p}{C_v}\right)$ for rigid molecules and $\gamma_2 = \left(\frac{C_p}{C_v}\right)$ for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct? (Cp and Cv are specific heats of the gas at constant pressure and volume)

$\gamma_A$ is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. $\gamma_B$ is the specific heat ratio of polyatomic gas $B$ having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If $\frac{\gamma_A}{\gamma_B} = \left(1 + \frac{1}{n}\right)$, then the value of $n$ is ________.

The ratio of the specific heats $\frac{C_p}{C_v} = \gamma$, in terms of degrees of freedom ( n) is

For a gas, $\frac{R}{C_v} = 0.4$ where R is the universal gas constant and ' $C_V$ ' is molar specific heat at constant volume. The gas is made up of molecules which are

If $C_p$ and $C_v$ are molar specific heats of an ideal gas at constant pressure and volume respectively and ' $\gamma$ ' is $C_p/C_v$ then $C_p =$ ( $R =$ universal gas constant)

According to the law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is

According to the law of equipartition of energy, the number of vibrational modes of a polyatomic gas of constant $\gamma = \frac{C_p}{C_v}$ is ($C_P$ and $C_V$ are the specific heat capacities of the gas at constant pressure and constant volume, respectively):

A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature $(27^\circ\text{C})$. The ratio of specific heat of gases at constant volume respectively is:

Two moles of a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is:

If three moles of monoatomic gas $\left(\gamma = \frac{5}{3}\right)$ is mixed with two moles of a diatomic gas $\left(\gamma = \frac{7}{5}\right)$, the value of adiabatic exponent $\gamma$ for the mixture is

The specific heat of argon at constant pressure and constant volume are $C_p$ and $C_v$ respectively. It's density ' $\rho$ ' at N.T.P. will be $[P$ and T are pressure and temperature respectively at N.T.P.]

The specific heat at constant pressure of a real gas obeying $PV^2 = RT$ equation is:

Four moles of hydrogen, two moles of helium and one mole of water vapour form an ideal gas mixture. $[C_v$ for hydrogen $= \frac{5}{2}R, C_v$ for helium $= \frac{3}{2}R, C_v$ for water vapour $= 3R]$ What is the molar specific heat at constant pressure of the mixture?

For polyatomic gases, the ratio of molar specific heat at constant pressure to constant volume is ( $f =$ degrees of freedom)

The molar specific heat of an ideal gas at constant pressure and constant volume is $C_p$ and $C_v$ respectively. If $R$ is universal gas constant and $\gamma = \frac{C_p}{C_v}$ then $C_v =$

For a gas, $\frac{R}{C_v} = 0.4$, where $R$ is universal gas constant and $C_v$ is molar specific heat at constant volume. The gas is made up of molecules which are

For a gas having '$X$' degrees of freedom, '$\gamma$' is ($\gamma =$ ratio of specific heats $= C_P/C_V$)

Let $\gamma_1$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and $\gamma_2$ be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio $\frac{\gamma_2}{\gamma_1}$ is

According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is :-

Let $\gamma_1$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and $\gamma_2$ be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio, $\frac{\gamma_1}{\gamma_2}$ is:

A gas has $n$ degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be:

The ratio of specific heats $\left(\frac{C_P}{C_V}\right)$ in terms of degree of freedom (f) is given by:

One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is $\frac{\alpha^2}{4}R\text{ J/mol K}$; then the value of $\alpha$ will be _________. (Assume that the given diatomic gas has no vibrational mode).

The amount of heat needed to raise the temperature of 4 moles of rigid diatomic gas from 0$^\circ$ C to 50$^\circ$ C when no work is done is ___________. (R is the universal gas constant).

Which one of the following is NOT a correct expression for an ideal gas?

[$C_p =$ Molar specific heat of a gas at constant pressure,

$C_v =$ Molar specific heat of a gas at constant volume,

$\gamma =$ Ratio of two specific heats of a gas,

$R =$ Universal gas constant]

For an ideal gas, $R = \frac{2}{3}C_v$. This suggests that the gas consists of molecules, which are [$R =$ universal gas constant]

For a gas molecule with 6 degrees of freedom, which one of the following relation between gas constant '$R$' and molar specific heat '$C_v$' is correct?

The molar specific heats of an ideal gas at constant pressure and volume are denoted by '$C_p$' and '$C_v$' respectively. If $\gamma = \frac{C_p}{C_v}$ and '$R$' is universal gas constant, then $C_v$ is equal to

Specific heats of an ideal gas at constant pressure and volume are denoted by $C_p$ and $C_v$ respectively. If $\gamma = \frac{C_p}{C_v}$ and $R$ it's the universal gas constant then $C_v$ is equal to

The correct relation between the degrees of freedom f and the ratio of specific heat $\gamma$ is:

For a gas CP $-$ CV = R in a state P and CP $-$ CV = 1.10 R in a state Q, TP and TQ are the temperatures in two different states P and Q respectively. Then

If one mole of the polyatomic gas is having two vibrational modes and $\beta$ is the ratio of molar specific heats for polyatomic gas $\left(\beta = \frac{C_P}{C_V}\right)$ then the value of $\beta$ is:

A polyatomic ideal gas has 24 vibrational modes. What is the value of $\gamma$?

For a gas, $\frac{R}{C_V} = 0.4$, where $R$ is universal gas constant and $C_V$ is the molar specific heat at constant volume. The gas is made up of molecules, which are

Match the $\frac{C_P}{C_V}$ ratio for ideal gases with different type of molecules:

Consider two ideal diatomic gases A and B at some temperature T. Molecules of the gas A are rigid, and have a mass m. Molecules of the gas B have an additional vibrational mode, and have a mass $\frac{m}{4}$. The ratio of the specific heats ($C_V^A$ and $C_V^B$) of gas A and B, respectively is:

Consider a mixture of n moles of helium gas and 2n moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its CP/CV value will be:

Two moles of an ideal gas with $\frac{C_P}{C_V} = \frac{5}{3}$ are mixed with 3 moles of another ideal gas with $\frac{C_P}{C_V} = \frac{4}{3}$. The value of $\frac{C_P}{C_V}$ for the mixture is:

If ' $C_P$ ' and ' $C_V$ ' are molar specific heats of an ideal gas at constant pressure and volume respectively. If ' $\gamma$ ' is the ratio of two specific heats and ' $R$ ' is universal gas constant then ' $C_p$ ' is equal to

The value of $\gamma \left(= \frac{C_p}{C_v}\right)$, for hydrogen, helium and another ideal diatomic gas X (whose molecules are not rigid but have an additional vibrational mode), are respectively equal to,

The specific heats, CP and CV of a gas of diatomic molecules, A, are given (in units of J mol–1 K–1) by 29 and 22, respectively. Another gas of diatomic molecules, B, has the corresponding values 30 and 21. If they are treated as ideal gases, then :-

Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume? (R = 8.3 J/mol K)

Two moles of helium are mixed with n moles of hydrogen. If $\frac{C_p}{C_v} = \frac{3}{2}$ for the mixture, then the value of n is:

An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure (Cp) and at constant volume (Cv) is:

CP and Cv are specific heats at constant pressure and constant volume respectively. It is observed that

CP – Cv = a for hydrogen gas

CP – Cv = b for nitrogen gas

The correct relation between a and b is

The ratio of the specific heats $\frac{C_p}{C_v} = \gamma$ in terms of degrees of freedom (n) is given by

Using equipartition of energy, the specific heat (in J kg${}^{-1}$ K${}^{-1}$) of aluminium at room temperature can be estimated to be (atomic weight of aluminium = 27)

If cp and cv denote the specific heats (per unit mass of an ideal gas of molecular weight M, then

If $C_p$ and $C_v$ denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then

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 gaseous mixture consists of $16\text{ g}$ of helium and $16\text{ g}$ of oxygen. The ratio $\frac{C_p}{C_v}$ of the mixture is

One mole of ideal monatomic gas $(\gamma = 5/3)$ is mixed with one mole of diatomic gas $(\gamma = 7/5)$. What is $\gamma$ for the mixture? $\gamma$ Denotes the ratio of specific heat at constant pressure, to that at constant volume

1 mole of a gas with $\gamma = 7/5$ is mixed with $1$ mole of a gas with $\gamma = 5/3,$ then the value of $\gamma$ for the resulting mixture is

If for a gas, $\frac{R}{C_V} = 0.67$, this gas is made up of molecules which are

For a certain gas the ratio of specific heats is given to be $\gamma = 1.5$. For this gas