A heat engine works at two temperature of 27 centigrade and 227 centigrade calculate the efficiency of the engine?

To calculate the efficiency of the engine, we can use the formula:

Efficiency = 1 - (Tc/Th)

Where:
Tc = temperature of the cold reservoir (27°C)
Th = temperature of the hot reservoir (227°C)

Converting the temperatures to Kelvin:
Tc = 27 + 273 = 300 K
Th = 227 + 273 = 500 K

Plugging the values into the formula:
Efficiency = 1 - (300/500)
Efficiency = 1 - 0.6
Efficiency = 0.4 or 40%

Therefore, the efficiency of the engine is 40%.

Given:

$$T_1=27 \degree C$$
$$T_2=227 \degree C$$
Where,

$$T_1$$ is the lower temperature in Celsius
$$T_2$$ is the higher temperature in Celsius

The efficiency of a heat engine is given by,
$$\eta=1-\frac{T_1}{T_2}$$

We need to convert the temperatures to Kelvin:
$$T_1=27 \degree C+273=300 K$$
$$T_2=227 \degree C+273=500 K$$

Substituting the values:
$$\eta=1-\frac{300 K}{500 K}$$
$$\eta=1-0.6$$
$$\eta=0.4$$

Therefore, the efficiency of the heat engine is 40%.