Question

Engine A receives three times more input heat, produces five times more work, and rejects two times more heat than engine B. Find the efficiency of (a) engine A and (b) engine B.

Answer 1

The efficiency of engine A is (5W / 3x) x 100%, and the efficiency of engine B is (W / x) x 100%.

Step-by-step explanation:

Engine A:

Let the input heat of engine B be x.

Input heat of engine A = 3 times the input heat of engine B = 3x

Output heat of engine B = x

Output heat of engine A = 2 times the output heat of engine B = 2x

Work done by engine B = W

Work done by engine A = 5 times the work done by engine B = 5W

Efficiency of engine = (Output work / Input heat) x 100%

(a) Efficiency of engine A:

Efficiency of engine A = (5W / 3x) x 100%

(b) Efficiency of engine B:

Efficiency of engine B = (W / x) x 100%

Answer 2

The efficiency of engine A is (5/3) times the efficiency of engine B.

Step-by-step explanation:

Let's denote the input heat of engine A as QA, the work produced by engine A as WA, and the heat rejected by engine A as QRA. Similarly, let's denote the input heat of engine B as QB, the work produced by engine B as WB, and the heat rejected by engine B as QRB.

According to the problem, we have the following relationships:

QA = 3QB

WA = 5WB

QRA = 2QRB

The efficiency of an engine is given by the ratio of the work produced to the input heat. Therefore, the efficiency of engine A (ηA) is equal to WA/QA and the efficiency of engine B (ηB) is equal to WB/QB.

Substituting the given relationships, we can solve for the efficiencies:

ηA = (5WB) / (3QB) = (5/3) * (WB/QB) = (5/3) * ηB

Therefore, the efficiency of engine A is (5/3) times the efficiency of engine B.