An engine has an efficiency of $0.25$ when temperature of sink is reduced by $58\,^oC$, if its efficiency is doubled, then the temperature of the source is ..... $^oC$
Diffcult
Download our app for free and get started
Here, $\eta_{1}=1-\frac{\mathrm{T}_{2}}{\mathrm{T}_{1}}$
$0.25=1-\frac{\mathrm{T}_{2}}{\mathrm{T}_{1}} \Rightarrow \frac{1}{4}=1-\frac{\mathrm{T}_{2}}{\mathrm{T}_{1}}$
$\frac{\mathrm{T}_{2}}{\mathrm{T}_{1}}=1-\frac{1}{4}=\frac{3}{4}$ $ . .(\mathrm{i})$
According to question.
$\eta_{2}=2 \eta_{1},$ and $\mathrm{T}_{2}=\mathrm{T}_{2}-58^{\circ} \mathrm{C}$
$\therefore \quad 2 \times \frac{1}{4}=1-\frac{\left(\mathrm{T}_{2}-58^{\circ} \mathrm{C}\right)}{\mathrm{T}_{1}}$
$\Rightarrow 1-\frac{1}{2}=\frac{\mathrm{T}_{2}-58^{\circ} \mathrm{C}}{\mathrm{T}_{1}}$
$\frac{1}{2}=\frac{T_{2}}{T_{1}}-\frac{58^{\circ}}{T_{1}} \Rightarrow \frac{3}{4}-\frac{1}{2}=\frac{58}{T_{1}}$
$\Rightarrow \mathrm{T}_{1}=232^{\circ} \mathrm{C}$
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
- 1One mole of ideal gas taken through a cycle process with alternate isothermal and adiabatic curves. In $P-V$ diagram $AB, CD, EF$ are isothermal curves at the absolute temperature $T_1, T_2$ and $T_3$ respectively and $BC, DE$ and $FA$ are adiabatic curves respectively. If $\frac{{{V_B}}}{{{V_A}}} = 2,\,\frac{{{V_D}}}{{{V_C}}} = 2$ then for cycle is shown in figure four statements are being made given below. (Figure is not drawn on scale)View Solution
Statement $1$ : Ratio of volumes $\frac{{{V_E}}}{{{V_F}}} = 4$
Statement $2$ : Magnitude of work done in isothermal compression $EF$ is $2RT_3\ ln\ (2)$
Statement $3$ : Ratio of heat supplied to gas in the process $AB$ to heat rejected by gas in process $EF$ is $\frac{{{T_1}}}{{2{T_3}}}$
Statement $4$ : Net work done by gas in the cycle $ABCDEFA$ is $(T_1 + T_2 - 2T_3) R\ ln\ (2)$
Find the number of correct statement $(s)$ given for the cyclic process followed by gas
- 2A diatomic gas undergoes a process represented by $PV ^{1.3}=$ constant. Choose the incorrect statementView Solution
- 3View SolutionWhich statement is incorrect?
- 4View SolutionWhich of the following is a slow process
- 5A cyclic process for $1\, mole$ of an ideal gas is shown in figure in the $V-T,$ diagram. The work done in $AB, BC$ and $CA$ respectivelyView Solution
- 6View SolutionAn adiabatic process occurs at constant
- 7$Assertion :$ In an isolated system the entropy increases.View Solution
$Reason :$ The processes in an isolated system are adiabatic. - 8A sample of gas with $\gamma=1.5$ is taken through an adiabatic process in which the volume is compressed from $1200\, {cm}^{3}$ to $300\, {cm}^{3}$. If the initial pressure is $200\, {kPa}$. The absolute value of the workdone by the gas in the process $= \,..... J.$View Solution
- 9The $P-V$ diagram of a system undergoing thermodynamic transformation is shown in figure. The work done on the system in going from $A → B → C$ is $50 J$ and $ 20\, cal$ heat is given to the system. The change in internal energy between $A$ and $C$ is ...... $J$View Solution
- 10Given 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