A reversible engine has an efficiency of $\frac{1}{4}$. If the temperature of the sink is reduced by $58^{\circ} \mathrm{C}$, its efficiency becomes double. Calculate the temperature of the $\sin k$ :
$174^{\circ} \mathrm{C}$
$280^{\circ} \mathrm{C}$
$180.4^{\circ} \mathrm{C}$
$382^{\circ} \mathrm{C}$
Correct Option: 1
$T_{2}=\operatorname{sink}$ temperature
$\eta=1-\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}$
$\frac{1}{4}=1-\frac{T_{2}}{T_{1}}$
$\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}=\frac{3}{4} \ldots$ (i)
$\frac{1}{2}=1-\frac{\mathrm{T}_{2}-58}{\mathrm{~T}_{1}}$
$\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}-\frac{58}{\mathrm{~T}_{1}}=\frac{1}{2}$
$\frac{3}{4}=\frac{58}{T_{1}}+\frac{1}{2}$
$\frac{1}{4}=\frac{58}{\mathrm{~T}_{1}} \Rightarrow \mathrm{T}_{1}=232$
$\mathrm{T}_{2}=\frac{3}{4} \times 232$
$T_{2}=174 \mathrm{~K}$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,