Heat engine X takes in four times more energy by heat from the hot reservoir than heat engine Y.

step 1 In this question, there are two heat engines, x and y. So we are given this relationship. So QH

Heat engine X takes in four times more energy by heat from...

Key Concepts

Heat Engine

A heat engine is a device that converts heat energy into mechanical work by absorbing heat from a high-temperature source and rejecting some of it to a low-temperature sink. This cyclic process is fundamental to understanding energy conversion, emphasizing how thermal energy is partly converted into useful work while the remainder is expelled.

Thermal Efficiency

Thermal efficiency is a key performance metric for heat engines, defined as the ratio of the work output to the amount of heat energy input from the high-temperature reservoir. It quantifies how effectively a heat engine converts the supplied thermal energy into mechanical work, with higher efficiencies indicating better performance.

First Law of Thermodynamics

The first law of thermodynamics, also known as the conservation of energy principle, states that energy within a closed system is conserved. For heat engines, this means the total energy input as heat is equal to the sum of the work output and the energy rejected as waste heat, forming the basis for calculating energy balances and efficiencies in thermodynamic cycles.

Energy Flow in Thermodynamic Cycles

Understanding the energy flow within a thermodynamic cycle involves accounting for energy absorbed as heat, work performed by the engine, and heat rejected to the surroundings. This analysis is crucial in both theoretical and practical applications, as it provides a framework for evaluating and comparing the performance of different heat engines.

Transcript

00:02 In this question, there are two heat engines, x and y.

00:05 So we are given this relationship.

00:09 So qh of x is 4 times of qh of y.

00:17 Okay.

00:20 And then you are also given that w engine of x is equal to 2 times the work done by engine of y and then we also know that qc of x is seven times the qc of y okay and then we always have this relationship qh is equal to w engine plus qc okay so that means that if look at x or heat engine x.

01:14 So in this question we need to find the efficiencies of heat engines x and y.

01:21 So for heat engine x we have qh x equals to w engine of x plus qc of x.

01:35 Okay.

01:37 So you can then try to find so in part a we need to find the efficiency of x, engine x, right? so one thing we know is that e of x is equal to w engine of x, devoured by qh of x.

02:00 Okay, so we need to try and see what we can do with, what we can find with w engine x and qh of x.

02:10 Okay, so, so if you substitute so you can proceed to do part a so we have qh of x equals to w engine of x plus qc of x so this is equal to 4 qh of y equals to 2 w engine of y plus 7 times of qc of y so notes that we also have qhy equals to w engine of y plus qc of y.

02:58 Okay, so this equality holds.

03:01 So if you look at this equation, we can actually obtain this.

03:08 2 qh of y equals to 5 qc of y.

03:13 So you just remove two engine of x and using this equation, okay, and then we can obtain this.

03:25 That means that qh of y is equal to 2 .5 qc of y.

03:38 Then the next thing is, so now we try to find wx, okay, in terms of qc, c, so we can find that given that qh of y is 2 .5 qc of y, right? so we can actually obtain so w and g not y.

04:26 It is going to be qh of y minus qc of y...

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