Question

The efficiency of a carnot cycle is 1/6. If on reducing the temperature of the sink 75 degree Celsius, the efficiency becomes 1/3, determine the initial and final temperature between which the cycle is working.

Answer 1

375 and 450

Step-by-step explanation:

The computation of the initial and the final temperature is shown below:

In condition 1:

The efficiency of a Carnot cycle is
`(1)/(6)`

So, the equation is

`(1)/(6) = 1 - (T_2)/(T_1)`

For condition 2:

Now if the temperature is reduced by 75 degrees So, the efficiency is
`(1)/(3)`

Therefore the next equation is

`(1)/(3) = 1 - (T_2 - 75)/(T_1)`

Now solve both the equations

solve equations (1) and (2)

`2(1 - T_2/T_1) = 1 - (T_2 - 75)/T_1\\\\2 - 1 = 2T_2/T_1 - (T_2 - 75)/T_1\\\\ = (T_2 + 75)/T_1T_1 = T_2 + 75\\\Now\ we\ will\ Put\ the\ values\ into\ equation (1)\\\\1/6 = 1 - T_2/(T_2 + 75)\\\\1/6 = (75)/(T_2 + 75)`

T_2 + 450 = 75

T_2 = 375

Now put the T_2 value in any of the above equation

i.e

T_1 = T_2 + 75

T_1 = 375 + 75

= 450