**Increasing the Efficiency of a Carnot Engine**

To increase the efficiency of a Carnot engine from 25 percent to 30 percent, we need to determine the degree by which the temperature of the source should be lowered.

**Understanding the Carnot Engine**

A Carnot engine is a theoretical engine that operates on the Carnot cycle, which consists of a series of four reversible processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression. The efficiency of a Carnot engine is given by the formula:

Efficiency = 1 - (Tc/Th)

Where Tc is the absolute temperature of the cold reservoir (sink) and Th is the absolute temperature of the hot reservoir (source).

**Calculating the Initial Temperatures**

Given that the efficiency of the Carnot engine is 25 percent, we can substitute this value into the efficiency formula and solve for Tc/Th:

0.25 = 1 - (Tc/Th)
Tc/Th = 1 - 0.25
Tc/Th = 0.75

**Calculating the Temperature Change**

To find the degree by which the temperature of the source should be lowered to increase the efficiency to 30 percent, we can set up the following equation:

0.3 = 1 - (Tc/(Th - ΔT))

Where ΔT represents the temperature change.

Simplifying the equation:

0.3 = 1 - (0.75/(Th - ΔT))

Rearranging the equation:

0.75/(Th - ΔT) = 0.7

Cross-multiplying:

0.75 = 0.7(Th - ΔT)

Expanding:

0.75 = 0.7Th - 0.7ΔT

Rearranging the equation:

0.7ΔT = 0.7Th - 0.75

Simplifying:

ΔT = (0.7Th - 0.75)/0.7

**Substituting the Values**

Now we can substitute the given temperature of the source (127 degrees Celsius) into the equation to find the temperature change:

ΔT = (0.7 * 127 - 0.75)/0.7

Calculating:

ΔT ≈ 121.79 degrees Celsius

Therefore, the temperature of the source should be lowered by approximately 121.79 degrees Celsius to increase the efficiency of the Carnot engine from 25 percent to 30 percent.

**Conclusion**

In summary, to increase the efficiency of a Carnot engine from 25 percent to 30 percent, the temperature of the source should be lowered by approximately 121.79 degrees Celsius. This calculation is based on the Carnot cycle and the efficiency formula. By understanding the principles of thermodynamics and the behavior of Carnot engines, we can determine the necessary temperature adjustments for optimizing their efficiency.