A reversible engine converts 1/6 of the heat input into work. When the temperature of the sink is reduced by 62C, the efficiency of the engine is doubled.What are the temperarure of the source and sink?

Efficiency η = W/Q = 1/6,

If T1 is the temperature of the source,
and T2 is the temperature of the sink,
η = (T1-T2)/T1 = 1- T2/T1
η = 1/6 = 1- T2/T1
2 η = 2/6 = (T1-(T2- 62))/T1 =1- (T2-62)/T1,
2/6 -1/6 = 1-(T2-62)/T1 – 1 - T2/T1.
1/6 = 62/T1
T1 = 372 K.
T2/T1 =1 – 1/6 = 5/6.
T2 = (5/6) •T1 = 310 K

To solve this problem, we need to use the formulas for the efficiency of a reversible engine and the change in efficiency when the temperature of the sink is changed.

The efficiency of a reversible engine can be calculated using the formula:

Efficiency = 1 - (Temperature of Sink / Temperature of Source)

Let's assume the initial temperatures of the source and sink are T_source and T_sink, respectively.

According to the given information, 1/6 of the heat input is converted into work, so the efficiency initially is 1/6. Using the above formula, we can write the initial efficiency equation as:

1/6 = 1 - (T_sink / T_source) ----(1)

Now, when the temperature of the sink is reduced by 62C, the efficiency is doubled. So we can set up the equation:

2 * (1/6) = 1 - (T_sink - 62) / T_source

Simplifying this equation gives:

1/3 = 1 - (T_sink - 62) / T_source ----(2)

Now, we can solve equations (1) and (2) simultaneously to find the values of T_source and T_sink.

First, let's solve equation (1):

1/6 = 1 - (T_sink / T_source)

Cross multiplying, we get:

T_sink = (6 * T_source) - T_source ----(3)

Now, let's substitute the value of T_sink from equation (3) into equation (2):

1/3 = 1 - ((6 * T_source) - T_source - 62) / T_source

Simplifying this equation gives:

1/3 = (T_source + 62) / T_source ----(4)

Multiplying both sides of equation (4) by T_source, we get:

T_source/3 = T_source + 62

On simplifying and rearranging terms, we have:

2 * T_source = 186

Dividing by 2, we find:

T_source = 93C

Now, let's substitute this value back into equation (3) to find the value of T_sink:

T_sink = (6 * T_source) - T_source

T_sink = (6 * 93) - 93

T_sink = 558 - 93

T_sink = 465C

Therefore, the initial temperature of the source is 93C and the temperature of the sink is 465C.