One mole of an ideal gas expands adiabatically from an initial state $\left(T_A, V_0\right)$ to final state $\left(T_f, 5 V_0\right)$. Another mole of the same gas expands isothermally from a different initial state ( $T_{\mathrm{B}}, \mathrm{V}_0$ ) to the same final state $\left(T_{\mathrm{f}}, 5 V_0\right)$. The ratio of the specific heats at constant pressure and constant volume of this ideal gas is $\gamma$. What is the ratio $T_{\mathrm{A}} / T_{\mathrm{B}}$ ?
IIT 2023, Easy
Download our app for free and get started
$\mathrm{T}_{\mathrm{A}} \mathrm{V}_0^{\gamma-1}=\mathrm{T}_{\mathrm{f}}\left(5 \mathrm{~V}_0\right)^{\gamma-1}$
$\frac{\mathrm{T}_{\mathrm{A}}}{\mathrm{T}_{\mathrm{f}}}=5^{\gamma-1}=\frac{\mathrm{T}_{\mathrm{A}}}{\mathrm{T}_{\mathrm{B}}}$
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
- 1View SolutionWhich of the following is not thermodynamical function
- 2One mole of an ideal gas expands at a constant temperature of $300 \,K$ from an initial volume of $10\, litres$ to a final volume of $20\, litres$. The work done in expanding the gas is ...... $J.$ $(R = 8.31 J/mole-K)$View Solution
- 3An ideal gas is taken through a quasi-static process described by $P = \alpha\, V^2$, with $\alpha = 5\,atm/m^6$. The gas is expanded to twice its original volume of $1\,m^3$. How much work is done by the expanding gas in this processView Solution
- 4View SolutionHeat energy absorbed by a system in going through a cyclic process shown in figure is
- 5Given that $1\,g$ of water in liquid phase has volume $1\,cm^3$ and in vapour phase $1671\, cm^3$ at atmospheric pressure and the latent heat of vaporization of water is $2256\,J/g;$ the change in the internal energy in joules for $1\,g$ of water at $373\,K$ when it changes from liquid phase to vapour phase at the same temperature is ....... $J$View Solution
- 6Half mole of an ideal monoatomic gas is heated at constant pressure of $1\, atm$ from $20\,^oC$ to $90\,^oC$. Work done by has is close to ..... $J$ (Gas constant $R = 8.31\, J/mol.K$)View Solution
- 7A Carnot engine works first between $200^{\circ} C$ and $0^{\circ} C$ and then between $0^{\circ} C$ and $-200^{\circ} C$. The ratio of its efficiency in the two cases isView Solution
- 8A system performs work $\Delta W$ when an amount of heat is$\Delta Q$ added to the system, the corresponding change in the internal energy is $\Delta U$. A unique function of the initial and final states (irrespective of the mode of change) isView Solution
- 9Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason $R$. Assertion A : Efficiency of a reversible heat engine will be highest at $-273^{\circ} C$ temperature of cold reservoir.View Solution
Reason $R$ : The efficiency of Carnot's engine depends not only on temperature of cold reservoir but it depends on the temperature of hot reservoir too and is given as $\eta=\left(1-\frac{ T _2}{ T _1}\right)$.
In the light of the above statements, choose the correct answer from the options given below
- 10A perfect gas goes from state $A$ to another state $B$ by absorbing $8 \times {10^5}J$ of heat and doing $6.5 \times {10^5}J$ of external work. It is now transferred between the same two states in another process in which it absorbs ${10^5}J$ of heat. Then in the second processView Solution