Question

A reversible power cycle operates with a thermal efficiency of 75%. The cycle receives energy input by heat from a thermal reservoir at 1200K. What is the temperature, in K, of the low temperature thermal reservoir

Answer 1

The temperature of the low temperature thermal reservoir is 300 K.

Step-by-step explanation:

All reversible power cycles are equivalent to the Carnot's cycle, whose equation for efficiency is:

`\eta_(th) =1-(T_(L))/(T_(H))` (Eq. 1)

Where:

`\eta_(th)` - Thermal efficiency, dimensionless.

`T_(H)` - High temperature reservoir, measured in Kelvin.

`T_(L)` - Low temperature reservoir, measured in Kelvin.

Now we proceed to clear the low temperature reservoir within:

`(T_(L))/(T_(H)) = 1-\eta_(th)`

`T_(L) = (1-\eta_(th))\cdot T_(H)`

If
`\eta_(th) = 0.75` and
`T_(H) = 1200\,K`, then:

`T_(L) = (1-0.75)\cdot (1200\,K)`

`T_(L) = 300\,K`

The temperature of the low temperature thermal reservoir is 300 K.