Question
A Carnot engine (E) is working between two temperatures 473 K and 273 K . In a new system two engines - engine $E_{1}$ works between 473 K to 373 K and engine $\mathrm{E}_{2}$ works between 373 K to 273 K . If $\eta_{12}$, $\eta_{1}$ and $\eta_{2}$ are the efficiencies of the engines $E, E_{1}$ and $\mathrm{E}_{2}$, respectively, then
(1) $\eta_{12}<\eta_{1}+\eta_{2}$ (2) $\eta_{12}=\eta_{1} \eta_{2}$
(3) $\eta_{12}=\eta_{1}+\eta_{2}$ (4) $\eta_{12} \geq \eta_{1}+\eta_{2}$

Answer

(1)
Sol. $\quad \eta_{12}=1-\frac{273}{473}=\frac{200}{473}=0.423$
$\eta_{1}=1-\frac{373}{473}=\frac{100}{473}=0.211$
$\eta_{2}=1-\frac{273}{373}=\frac{100}{373}=0.268$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

A current $i$ ampere flows along the inner conductor of a coaxial cable and returns along the outer conductor of the cable, then the magnetic induction at any point outside the conductor at a distance $r$ metre from the axis is
Moment of inertia of a uniform hollow hemi-sphere about given axis is $I_A$ and $I_B$ then
${f_V}$ and ${f_R}$ are the focal lengths of a convex lens for violet and red light respectively and ${F_V}$ and ${F_R}$ are the focal lengths of a concave lens for violet and red light respectively, then
A metallic bar of Young's modulus, $0.5 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$ and coefficient of linear thermal expansion $10^{-5}{ }^{\circ} \mathrm{C}^{-1}$, length $1 \mathrm{~m}$ and area of cross-section $10^{-3} \mathrm{~m}^2$ is heated from $0^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C}$ without expansion or bending. The compressive force developed in it is :
If two moles of diatomic gas and one mole of mono atomic gas are mixed then the ratio of specific heats $\gamma=$ ......
For a domestic AC supply of $220 \,V$ at $50 \,cps$, the potential difference between the terminals of a two-pin electric outlet in a room is (in volt) given by
An infinite, uniformly charged sheet with surface charge density $\sigma$ cuts through a spherical Gaussian surface of radius $R$ at a distance $x$ from its center, as shown in the figure. The electric flux $\Phi $ through the Gaussian surface is
The distance of the Sun from earth is $1.5 \times 10^{11} \,m$ and its angular diameter is $(2000) \,s$ when observed from the earth. The diameter of the Sun will be ...........
Light ray is incident on a prism of angle $A= 60^o$ and refractive index $\mu =\sqrt 2 $ The angle of incidence at which the emergent ray grazes the surface is given by . 
Construction of submarines is based on