Question

Which of the following is the most effective way to increase the efficiency of the carnotengine ?

• A. To increase the temperature of heat reservoir
• B. To decrease the temperature of heat sink
• C. To increase the temperature of heat sink
• D. To decrease the temperature of heat reservoir

Answer 1

Answer: (B)

To decrease the temperature of heat sink

Answer 2

Let temperature of heat reservoir and heat sink are T₁ and T₂ respectively.

h = 1 – $\frac{T_{2}}{T_{1}}$

Let T₂ is reduced by DT, hence

h₁ = 1 – $\frac{(T_{2}–\Delta T)}{T_{1}}$

Let in other case T₁ is increased by DT, hence,

h₂ = 1 – $\frac{T_{2}}{(T_{1} + \Delta T)}$

h₁ – h₂ = 1 – $\frac{(T_{2}–\Delta T)}{T_{1}}$ – 1+ $\frac{T_{2}}{(T_{1} + \Delta T)}$

or h₁ – h₂ = $\frac{T_{2}}{(T_{1} + \Delta T)}$ – $\frac{(T_{2}–\Delta T)}{T_{1}}$

= $\frac{(T_{1}–T_{2})\Delta T + (\Delta T)^{2}}{T_{1}(T_{1} + \Delta T)}$

since T₁ > T₂, hence h₁ > h₂