Question

A Carnot engine operating between a reservoir of liquid mercury at its melting point (233 K) and a colder reservoir extracts 10.0 J of heat from the mercury and does 8.0 J of work during each cycle. What is the temperature of the colder reservoir

Answer 1

Answer:

T'=46.6 K              

Explanation:

Let T be the temperature of a hot reservoir, T' be the temperature of cold reservoir.

For a Carnot's engine, efficiency can be calculated as follows:

$\eta=\frac{W}{Q}=1-\frac{T'}{T}$

Where, W is the amount of work done, Q is the amount of heat extracted from the hot reservoir.

Substitute the values: W= 8.0 J

Q = 10.0 J

T = 233 K

$\frac{8}{10}=1-\frac{T'}{233K}\\\Rightarrow 0.8 = 1-\frac{T'}{233K}\\\\\Rightarrow T' = 0.2 \times 233 K\\\Rightarrow T'=46.6 K$

Thus, the temperature of the cold reservoir is 46.6 K.