Name: Introduction to First Law of Thermodynamics
Uploaded: 2019-07-19
Duration: 7 min 10 s
Description: The video defines the first law of thermodynamics and explains the relation between the total kinetic energy and the internal energy of a gas. Watch on!

Question

In a heat engine, the temperature of the source and sink are,

500 K

and

375 K

. If the engine consumes

25 \times 10^{5} J

per cycle, find (a) the efficiency of the engine, (b) work done per cycle, and (c) heat rejected to the sink per cycle.

Accepted Answer

Heat engine is the device which converts heat into work.
Carnot engine is an ideal heat engine.
Efficiency of an ideal heat engine is given by $η$ .
$η = \frac{work done by gas during a cycle}{heat absorbed during that cycle}$ .

Block diagram of heat engine:
$T_{1} =$ temperature of source from where heat is absorbed,
$T_{2} =$ temperature of sink in which heat is rejected,
$Q_{1} =$ amount of heat absorbed by the engine from the source,
$Q_{2} =$ amount of heat rejected to sink by the engine.

From conservation of energy,
heat absorbed $=$ work done by the gas $+$ heat rejected.

$Q_{1} = W + Q_{2}$
$W = Q_{1} - Q_{2}$ .
$∴$ Efficiency of engine,
$η = \frac{W}{Q_{1}}$
$= \frac{Q_{1} - Q_{2}}{Q_{1}}$
$= 1 - \frac{Q_{2}}{Q_{1}}$ .
For carnot cycle,

$= \frac{Q_{1}}{Q_{2}} = \frac{T_{1}}{T_{2}}$
$∴ η = 1 - \frac{T_{2}}{T_{1}} = \frac{W}{Q_{1}}$ .

Temperature of $T_{1} = 500 K$ ,
Temperature of $T_{2} = 375 K$ ,
$Q = 25 \times 10^{5} J$ .
Efficiency of cycle $= 1 - \frac{T_{2}}{T_{1}}$
$= 1 - \frac{375}{500}$
$= 1 - \frac{15}{20}$
$= \frac{1}{4} = 0 .25$
$= 25 %$ .

$η = \frac{W}{Q_{1}} = \frac{1}{4}$
$W = \frac{Q_{1}}{4} = \frac{25}{4} \times 10^{5} J$
$= 6 .25 \times 10^{5} J$ .

Heat rejected, $Q_{2} = Q_{1} - W$
$= (25 - \frac{25}{4}) 10^{5} J$
$= 25 \times \frac{3}{4} \times 10^{5} J$
$= \frac{75}{4} \times 10^{5} J$
$= 18.75 \times 10^{5} J$ .

D. C. Pandey Solutions for Chapter: Laws of Thermodynamics, Exercise 4: INTRODUCTORY EXERCISE 21.4

D. C. Pandey Physics Solutions for Exercise - D. C. Pandey Solutions for Chapter: Laws of Thermodynamics, Exercise 4: INTRODUCTORY EXERCISE 21.4

Questions from D. C. Pandey Solutions for Chapter: Laws of Thermodynamics, Exercise 4: INTRODUCTORY EXERCISE 21.4 with Hints & Solutions

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