(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A reversible hear engine, operating in a cycle, withdraws heat from a high temperature reservoir (temperature consequently decreases). It performs work w, and rejects heat into a low-temperature reservoir(temperature consequently increases).

The 2 reservoirs are initially at temperatures T1 and T2 and have constant heat capacities C1 and C2. Calculate the final temperature of the system and the Wmax from the engine.

2. Relevant equations

W = q2 - q1

Wmax = Qrev

ΔU = ΔH = 0

C = q/ΔT or dq/DT

q = nCpDT

(q2 - q1)/q2 = (t2 - t1)/t2

3. The attempt at a solution

I'm having a hard time understanding what I'm doing from a conceptual perspective and in terms of explanation.

q2 = 1 mole * C2 * (Tf-T2)

q1 = 1 mole * C1 * (Tf-T1)

w = q2 - q1

w = C2(Tf-T2) - [C1(Tf-T1)] **(The answer has the C2 term negative, Is it because heat from the reservoir is added to the heat engine?)

This process continues until T1=T2 @ T.

Efficiency = w/q2 = 1 - q1/q2.

dW/dq_2 = (q2 - q1) / q2 = (T2 - T1) / T2

dW = (T2 - T1) / dQ_2

**I get stuck here. Do we split this into 2 integrals (1 for dT1 and the other for dT2?) I have to find a way to relate the heat q2 to the temperatures of T1 and T2. (q2 = T - T2 and q2T1 = q1T2, am I on the right track?). Help would be much appreciated.

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# Homework Help: Reversible(Carnot) Cycle Temperature Equilibrium Problem

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