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.
If $$\alpha$$ is the polytropic index then
$$pV^{\alpha}$$ = constant, $$TV^{\alpha - 1}$$ = constant.
Now, $$\frac{v'}{v} = \frac{n'}{n} \frac{
Hence, $$\frac{1}{\alpha - 1} = -\frac{1}{2}$$ or $$\alpha = -1$$
Then $$C = \frac{iR}{2} + \frac{R}{2} = 3R$$
Consider two ideal diatomic gases A and B at some temperature T. Molecules of the gas A are rigid, and have a mass m. Molecules of the gas B have an additional vibrational mode, and have a mass $$\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.
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.
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