Compare two methods to improve the theoretical efficiency of a heat engine: lower the exhaust temperature tc by 10 k, or raise the input temperature th by 10 k. which method would result in the greater increase in efficiency?
both changes would give the same result.
there is nothing you can do to improve the theoretical efficiency of a heat engine.
the best method would depend on the difference between tc and th.
lower tc by 10 k.
raise th by 10 k.

both changes give the same result

Explanation:

The efficiency of a thermal machine

       e = W / Q = 1 - /

E heat in calorimetries

      Q = m T

By replacing in education it remains

     e = 1 - /

Where T is the temperature of the cold focus and Th is the temperature of the hot focus

Let's apply the changes

Let's call eo the initial efficiency

     eo = 1 - /

10K cold focus decrease

      ’=   - 10

     e’= 1 - ( -10) /  

     e’= (1 - / ) + 10 /  

     e’= e₀ + 10 /  

Increase of hot spot in 10K

    ’= + 10

    e’’ = 1 - / ( +10)

    e’’ = 1- / (1 + 10 / )

    e’’ = 1- / (1 + 10 / )⁻¹

In general Th is of the order of 300 to 500K whereby the 10K incense is small bone 10 / Th << 1, therefore, we can make a serious expansion

     (1+ x)⁻¹ = 1 + (- 1) x +…

It is our case remains

    (1+ 10 / Th)⁻¹ = 1 - 10 /

Substituting

    e’’ = 1 - / (1- 10 / )

    e’’ = 1- / + 10 /

    e’’ = e₀ + 10 /

We can see that the two efficiencies are equal (e ’= e'' )

Let's review the claims

A) True. both changes give the same result

B) False. Theoretical efficiency depends on the temperatures of the foci

C) True. True while more difference is better in efficiency Th >> Tc

D) False are the same

E) False They are the same

i would say the answer is food.

hope this !