One mole of a monoatomic ideal gas is mixed with one mole of a diatomic ideal gas. The molar specific heat of the mixture at constant volume is
$$ (C_V)_{mix} = \dfrac{\mu_1 C_{V_1} + \mu_2 C_{V_2}}{\mu_1 + \mu_2} = \dfrac{1 \times \dfrac{3}{2} R + 1 \times \dfrac{5}{2}R}{1 + 1} = 2R$$
$$ \left ((C_V)_{mono} = \dfrac{3}{2} R, (C_V)_{di} = \dfrac{5}{2} R \right ) $$
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 $$\dfrac{m}{4}$$. The ratio of the specific heats$$(C^A_V$$ and $$C^B_V)$$ of gas A and B, respectively is?
A diatomic gas with rigid molecules does $$10 J$$ of work when expanded at constant pressure. What would be the heat energy absorbed by the gas, in this process ?
An amount Q of heat is added to a monatomic ideal gas in a process in which the gas perfomrs a work Q/2 on its surrounding.Find the molar heat capacity for the process.
$$1\ kg$$ of ice at $$0^{\circ}C$$ is mixed with $$1\ kg$$ of steam at $$100^{\circ}C$$. What will be the composition of the system when thermal equilibrium is reached? Latent of fusion $$3.36\times 10\ J/ g $$ and latent heat of vaporization of water = $$2.26\times 10\ J/ g $$.
Three moles of an ideal monoatomic gas perform a cycle as shown in the figure. The gas temperature in different states are : $$T_1= 400 \ K, \ T_2 = 800 \ K, \ T_3 = 2400 \ K \ \ $$ and $$\ \ T_4 =1200 \ K.$$ The work done by the gas during the cycle is:
What is the molar heat capacity for the process, when $$10\ J$$ of heat added to a monoatomic ideal gas in a process in which the gas performs a work of $$5\ J$$ on its surrounding ?
In a certain polytropic process the volume of argon was increased $$\alpha = 4.0$$ times. Simultaneously, the pressure decreased $$\beta = 8.0 $$ times. Find the molar heat capacity of argon in this process, assuming the gas to be ideal.
Suppose a gas is heated up to a temperature at which all degrees of freedom (translational, rotational, and vibrational) of its molecules are excited. Find the molar heat capacity of such a gas in the isochoric process, as well as the adiabatic exponent $$\gamma$$, if the gas consists of (a) diatomic; (b) linear N-atomic; (c) network N-atomic molecules.
A gas consisting of rigid diatomic molecules was expanded in a polytropic process so that the rate of collisions of the molecules against the vessel's wall did not change. Find the molar heat capacity of the gas in this process.
Determine the molar heat capacity of a polytropic process through which an ideal gas consisting of rigid diatomic molecules goes and in which the number of collisions between the molecules remains constant (a) in a unit volume; (b) in the total volume of the gas.