Question:
A heat engine operates between a cold reservoir at temperature $\mathrm{T}_{2}=400 \mathrm{~K}$ and a hot reservoir at temperature $\mathrm{T}_{1}$. It takes $300 \mathrm{~J}$ of heat from the hot reservoir and delivers $240 \mathrm{~J}$ of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be_____________K.
Solution:
$Q_{\text {in }}=300 \mathrm{~J} ; \mathrm{Q}_{\text {out }}=240 \mathrm{~J}$
Work done $=Q_{\text {in }}-Q_{\text {out }}=300-240=60 \mathrm{~J}$
Efficiency $=\frac{\mathrm{W}}{\mathrm{Q}_{\mathrm{in}}}=\frac{60}{300}=\frac{1}{5}$
efficiency $=1-\frac{T_{2}}{T_{1}}$
$\frac{1}{5}=1-\frac{400}{\mathrm{~T}_{1}} \Rightarrow \frac{400}{\mathrm{~T}_{1}}=\frac{4}{5}$
$\mathrm{T}_{1}=500 \mathrm{k}$
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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,
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