Heat and Thermodynamics

In an adiabatic process, the density of a diatomic gas becomes 32 times its initial value. The final pressure of the gas is found to be n times the initial pressure. The value of n is :

Given below are two statements: Statement (I) : Dimensions of specific heat is $[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}]$. Statement (II) : Dimensions of gas constant is $[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-1} \mathrm{~K}^{-1}]$. In the light of the above statements, choose the most appropriate answer from the options given below.

The specific heat at constant pressure of a real gas obeying $P V^2=R T$ equation is:

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio ${C_p}/{C_V}$ for the gas is

The work of $146$ $kJ$ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by ${7^ \circ }C.$ The gas is $\left( {R = 8.3J\,\,mo{l^{ - 1}}\,{K^{ - 1}}} \right)$

Consider a spherical shell of radius $R$ at temperature $T$. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume $u = {U \over V}\, \propto \,{T^4}$ and pressure $p = {1 \over 3}\left( {{U \over V}} \right)$ . If the shell now undergoes an adiabatic expansion the relation between $T$ and $R$ is:

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity $C$ remains constant. If during this process the relation of pressure $P$ and volume $V$ is given by $P{V^n} =$ constant, then $n$ is given by (Here ${C_p}$ and ${C_v}$ are molar specific heat at constant pressure and constant volume, respectively:

The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is :

Two moles of an ideal monatomic gas occupies a volume V at 27^oC. The gas expands adiabatically to a volume 2 V. Calculate (a) the final temperature of the gas and (b) change in its internal energy.

One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, ${27^ \circ }C.$ The work done on the gas will be :