Question 12.7:
A steam engine delivers 5.4×108 J of work per minute and services 3.6 × 109 J of heat per minute from its boiler. What is the efficiency of the engine? How much heat is wasted per minute?
Answer:
Work done by the steam engine per minute, W = 5.4 × 108 J
Heat supplied from the boiler, H = 3.6 × 109 J
Efficiency of the engine =
Hence, the percentage efficiency of the engine is 15 %.
Amount of heat wasted = 3.6 × 109 – 5.4 × 108
= 30.6 × 108 = 3.06 × 109 J
Therefore, the amount of heat wasted per minute is 3.06 × 109 J.
Question 12.8:
An electric heater supplies heat to a system at a rate of 100W. If system performs work at a rate of 75 Joules per second. At what rate is the internal energy increasing?
Answer:
Heat is supplied to the system at a rate of 100 W.
∴Heat supplied, Q = 100 J/s
The system performs at a rate of 75 J/s.
∴Work done, W = 75 J/s
From the first law of thermodynamics, we have:
Q = U + W
Where,
U = Internal energy
∴U = Q – W
= 100 – 75
= 25 J/s
= 25 W
Therefore, the internal energy of the given electric heater increases at a rate of 25 W.
Question 12.9:
A thermodynamic system is taken from an original state to an intermediate state by the linear process shown in Fig. (12.13)
Its volume is then reduced to the original value from E to F by an isobaric process. Calculate the total work done by the gas from D to E to F
Answer:
Total work done by the gas from D to E to F = Area of ΔDEF
Area of ΔDEF =
Where,
DF = Change in pressure
= 600 N/m2 – 300 N/m2
= 300 N/m2
FE = Change in volume
= 5.0 m3 – 2.0 m3
= 3.0 m3
Area of ΔDEF = = 450 J
Therefore, the total work done by the gas from D to E to F is 450 J.
Question 12.10:
A refrigerator is to maintain eatables kept inside at 9°C. If room temperature is 36° C, calculate the coefficient of performance.
Answer:
Temperature inside the refrigerator, T1 = 9°C = 282 K
Room temperature, T2 = 36°C = 309 K
Coefficient of performance =
Therefore, the coefficient of performance of the given refrigerator is 10.44.