Question

A certain solar energy collector produces a maximum temperature of 100°C. The energy is used in a cyclic heat engine that operates in a 10°C environment. What is the maximum thermal efficiency? What is it if the collector is redesigned to focus the incoming light to produce a maximum temperature of 300°C?

Answer 1

`\eta _(max) = 0.2413 = 24.13%`

`\eta' _(max) = 0.5061 = 50.61%`

Given:

`T_(1max) = 100^(\circ) = 273 + 100 = 373 K`

operating temperature of heat engine,
`T_(2) = 10^(\circ) = 273 + 10 = 283 K`

`T_(3max) = 300^(\circ) = 273 + 300 = 573 K`

Solution:

For a reversible cycle, maximum efficiency,
`\eta _(max)` is given by:

`\eta _(max) = 1 - (T_(2))/(T_(1max))`

`\eta _(max) = 1 - (283)/(373) = 0.24`

`\eta _(max) = 0.2413 = 24.13%`

Now, on re designing collector, maximum temperature,
`T_(3max)` changes to
`300^(\circ)`, so, the new maximum efficiency,
`\eta' _(max)` is given by:

`\eta' _(max) = 1 - (T_(2))/(T_(3max))`

`\eta _(max) = 1 - (283)/(573) = 0.5061`

`\eta _(max) = 0.5061 = 50.61%`