During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of $\frac{C_p}{C_V}$ for the gas is:
JEE MAIN 2024, Diffcult
Download our app for free and get started
$\mathrm{P} \propto \mathrm{T}^3$
$\mathrm{PT}^{-3}=\text { constant }$
$\because \frac{\mathrm{PV}}{\mathrm{T}}=\mathrm{nR}=\text { constant from ideal gas equation }$
$(\mathrm{P})(\mathrm{PV})^{-3}=\text { constant }$
$\mathrm{P}^{-2} \mathrm{~V}^{-3}=\text { cosntant } \quad . .(1)$
$\because \text { Process equation for adiabatic process is }$
$\mathrm{PV}^y=\text { constant } \quad . .(2)$
$\text { Comparing equation (1) and (2) }$
$\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{V}}}=\mathrm{y}=\frac{3}{2}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1Areversible adiabatic path on a $P-V$ diagram for an ideal gas passes through stateAwhere $P=0$.$7\times 10^5 \,\,N/ m^{-2}$ and $v = 0.0049 \,\,m^3$. The ratio of specific heat of the gas is $1.4$. The slope of path at $A$ is :View Solution
- 2View SolutionA given system undergoes a change in which the work done by the system equals the decrease in its internal energy. The system must have undergone an
- 3View SolutionThe temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is
- 4In case of an adiabatic process the correct relation in terms of pressure $p$ and density $\rho $ of a gas isView Solution
- 5A shown in the figure, the amount of heat absorbed along the path $ABC$ is $90\,J$ and the amount of work done by the system is $30\,J$ . If the amount of work done along the path $ADC$ is $20\,J$ , the amount of heat absorbed will be .... $J$View Solution
- 6View SolutionWhich of the following laws of thermodynamics defines the term internal energy?
- 7A bicycle tyre is filled with air having pressure of $270\,kPa$ at $27^{\circ}\,C$. The approximate pressure of the air in the tyre when the temperature increases to $36^{\circ}\,C$ is $............kPa$View Solution
- 8A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from $V$ to $32\ V$, the efficiency of the engine isView Solution
- 9A thin piece of thermal conductor of constant thermal conductivity insulated on the lateral sides connects two reservoirs which are maintained at temperatures $T_{1}$ and $T_{2}$ as shown in the figure alongside. Assuming that the system is in steady state, which of the following plots best represents the dependence of the rate of change of entropy on the ratio of $T_{1} / T_{2}$ ?View Solution
- 10View SolutionAn ideal gas undergoes a cyclic process as shown in diagram. The net work done by the gas in the cycle is
