**Temperature of Sink and Efficiency of a Heat Engine**

When discussing the temperature of a heat engine, we refer to the temperatures of the heat source and heat sink. The heat engine operates by converting thermal energy from a high-temperature heat source to mechanical work, with the low-temperature heat sink absorbing the waste heat.

The efficiency of a heat engine is defined as the ratio of the work output to the heat input. It can be calculated using the formula:

Efficiency = (Work output / Heat input) * 100%

Given that the efficiency of the heat engine is 40%, and the temperature of the sink (Ts) is 27°C, we can determine the temperature of the heat source (Th).

**Calculating the Efficiency:**

To calculate the efficiency, we need to know the values of the work output and heat input. However, in this scenario, we only have the efficiency value.

We can use the efficiency formula to rearrange and solve for the work output:

Efficiency = (Work output / Heat input) * 100%
40% = (Work output / Heat input) * 100%

Since we don't know either the work output or heat input, we cannot determine their values directly.

**Using the Carnot Efficiency:**

The Carnot efficiency is a theoretical maximum efficiency for a heat engine operating between two temperatures. It is given by the formula:

Carnot Efficiency = 1 - (Temperature of Sink / Temperature of Source)

We can rearrange this equation to solve for the temperature of the source:

Temperature of Source = Temperature of Sink / (1 - Carnot Efficiency)

**Calculating the Temperature of the Source:**

Given that the temperature of the sink is 27°C and the efficiency is 40%, we can substitute these values into the Carnot efficiency formula:

Temperature of Source = 27 / (1 - 0.40)
Temperature of Source = 27 / 0.60
Temperature of Source = 45°C

Therefore, the temperature of the heat source is 45°C.

**Explanation:**

The efficiency of a heat engine is determined by the temperature difference between the heat source and heat sink. The higher the temperature difference, the higher the efficiency. In this scenario, we only know the temperature of the sink and the efficiency, but by using the Carnot efficiency formula, we can calculate the temperature of the source.

The Carnot efficiency represents the maximum achievable efficiency for a heat engine operating between two temperatures. By rearranging the formula, we can solve for the temperature of the source, given the temperature of the sink and the known efficiency.

In conclusion, with a sink temperature of 27°C and an efficiency of 40%, the temperature of the heat source is calculated to be 45°C.