This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement $1 :$ An inventor claims to have constructed an engine that has an efficiency of $30\%$ when operated between the boiling and freezing points of water. This is not possible.
Statement $2:$ The efficiency of a real engine is always less than the efficiency of a Carnot engine operating between the same two temperatures.
AIEEE 2012, Diffcult
Download our app for free and get started
According to Carnot's theorem $-$ no heat engine working between two given temperatures of source and sink can be more efficient than a perfectly reversible engine i.e. Carnot engine working between the same two temperatures.
Efficiency of Carnot's engine, $n=1-\frac{T_{2}}{T_{1}}$
$ where, T_{1}= temperature \,of\, source $
$T_{2}= temperature of \sin k$
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
- 1Two Carnot engines $A$ and $B$ are operated in succession. The first one, $A$ receives heat from a source at ${T_1} = 800K$ and rejects to sink at ${T_2}K.$. The second engine $B$ receives heat rejected by the first engine and rejects to another sink at ${T_3} = 300K.$ If the work outputs of two engines are equal, then the value of ${T_2}$ is .... $K$View Solution
- 2A mixture of gases at $STP$ for which $\gamma=1.5$ is suddenly compressed to $\frac{1}{9}$ th of its original volume. The final temperature of mixture is .......... $^{\circ} C$View Solution
- 3An ideal gas of density $\rho=0.2 kg m ^{-3}$ enters a chimney of height $h$ at the rate of $\alpha=0.8 kg s ^{-1}$ from its lower end, and escapes through the upper end as shown in the figure. The cross-sectional area of the lower end is $A_1=0.1 m ^2$ and the upper end is $A_2=0.4 m ^2$. The pressure and the temperature of the gas at the lower end are $600 Pa$ and $300 K$, respectively, while its temperature at the upper end is $150 K$. The chimney is heat insulated so that the gas undergoes adiabatic expansion. Take $g=10 ms ^{-2}$ and the ratio of specific heats of the gas $\gamma=2$. Ignore atmospheric pressure.View Solution
Which of the following statement($s$) is(are) correct?
- 4A Carnot engine, whose efficiency is $40\%$, takes in heat from a source maintained at a temperature of $500\ K$. It is desired to have an engine of efficiency $60\%$. Then, the intake temperature for the same exhaust (sink) temperature must be ....... $K$View Solution
- 5Consider the following volume-temperature $( V - T )$ diagram for the expansion of $5$ moles of an ideal monoatomic gas.View Solution
Considering only $P-V$ work is involved, the total change in enthalpy (in Joule) for the transformation of state in the sequence $X \rightarrow Y \rightarrow Z$ is $\qquad$
[Use the given data: Molar heat capacity of the gas for the given temperature range, $C _{ v , m }=12 J K ^{-1} mol ^{-1}$ and gas constant, $R =8.3 J K ^{-1} mol ^{-1}$ ]
- 6The $P-V$ diagram of $2$ gm of helium gas for a certain process $A \to B$ is shown in the figure. what is the heat given to the gas during the process $A \to B$View Solution
- 7A Carnot engine absorbs $1000\,J$ of heat energy from a reservoir at $127\,^oC$ and rejects $600\,J$ of heat energy during each cycle. The efficiency of engine and temperature of sink will beView Solution
- 8The efficiency of the cycle shown below in the figure (consisting of one isobar, one adiabat and one isotherm) is $50 \%$. The ratio $x$, between the highest and lowest temperatures attained in this cycle obeys (the working substance is an ideal gas)View Solution
- 9Following figure shows two processes $A$ and $B$ for a gas. If $\Delta Q_A$ and $\Delta Q_B$ are the amount of heat absorbed by the system in two cases, and $\Delta U_A$ and $\Delta U_B$ are changes in internal energies, respectively, thenView Solution
- 10View SolutionDuring the thermodynamic process shown in figure for an ideal gas
