Engineers are always searching for ways to make heat

Question

Maximum Efficiency of an Engine

Engineers are always searching for ways to make heat engines more efficient. The ideal heat engine would convert all the heat absorbed into work. According to the Second Law of Thermodynamics, however, no heat engine can have 100% efficiency. In 1824, the French engineer Sadi Carnot (1796-1832) determined the maximum possible efficiency of a heat engine allowed by the second law. This maximum possible efficiency is called the Carnot efficiency, e_Carnot. The Carnot efficiency depends only on the temperatures of the hot and cold baths, sometimes called reservoirs. The Carnot efficiency is given by ^eCarnot = 1 - T_cold / T_hot

where T_Hot is the temperature of the hot reservoir and T_Cold is the temperature of the cold reservoir. There is one special consideration, however. The temperature must be expressed using the Kelvin temperature scale. The Kelvin scale is named for the British physicist Lord Kelvin (1824-1907). The Kelvin scale is related to the Celsius scale through the relationship

T_k - T_c + 273.15

where T_K is the temperature in kelvins (K) and T_C is the temperature in degrees celcius (°C).

1. For the heat engine used in this experiment, the temperatures of the hot bath and the cold bath were

T_Hot = 80 °C and T_Cold = 0 °C, respectively. Calculate T_Hot and T_Cold in kelvins.

2. Calculate the Carnot efficiency for this heat engine.