Question

9. Which of the following statements is FALSE? I. The efficiency of a heat engine has no units II. The coefficient of performance of a heat pump has no units III. The coefficient of performance can be less than 1 IV. The Carnot efficiency of a heat engine can be increased by decreasing the temperature difference between the cold and hot reservoir a. I and II b. II and III c. Only III d. III and IV e. II and IV

Answer 1

So Lets talk about each and every point individually.

I. Efficiency of any system is measured by the ratio of the output produced by the system to the input given to the system. So in the case of heat engine the given by the ratio of amount of work done by the engine for given heat input as both the quantity has same dimensions so genrally the efficiency of any system is unitless quantity. So for the case of heat engine also the efficiency ha no units. So I is true.

II. As we know that Coefficient of performance(COP) is given by the ratio of heating effect to the work input .i.e. COP_HP = Q_H / Win . futher using first law of thermodynamics it can be reduced to COP_HP = Q_H / (Q_H - Q_C ) it can be clearly seen that COP is unitless quantity. hence II is true

III. Coefficient of performance(COP) is given by the ratio of heating effect to the work input and the COP_HP is related to COP of refrigrator as : COP_HP = COP_R + 1 and we know that COP_R is always positive which implies that COP_HP > 1 always, there is no case when COP_HP is < 1. So III is False.

IV. If we look at the formula for carnot efficiency for heat engine in terms of temprature is : N = (T_H - T_C)/T_H  from here we can observe that the carnot efficiency is directly proportional to the temprature difference between hot and cool reservior hence on decresing the temprature difference between the two reserviors the carnot efficiency decreases. hence IV is false.

So from all the above points we can conclude that statements III and IV are False. hence D is correct option.