# Two objects exchange heat through a cyclical thermal machine

• ValeForce46
In summary, for part a), the quantity of exchanged heat for the machine is calculated by subtracting the heat lost by object 1 and the heat absorbed by object 2. From the first law of thermodynamics, it is determined that the heat absorbed by object 2 is equal to the heat lost by object 1 minus the work done. The temperature of object 2 can be calculated using the heat absorbed, the heat capacity, and the initial temperature. For part b), the relation ##\frac{Q_1}{Q_2}=\frac{T_1}{T_2}## must be used to solve the problem.
ValeForce46
Homework Statement
Two object (thermal capacity ##C=3\cdot10^3 \frac{J}{K}##) are initially at the same temperature ##T_i=450 K##, and they're linked through a cyclical thermal machine.

a) One of the two object is cooled down at the temperature ##T_1=300 K## and the work done by the machine is ##W=6\cdot10^4 J##. Calculate the temperature ##T_2## of the second object when the first reachs ##T_1##.

b)Assume, now, that the thermal machine is reversible and the first object reachs ##T_1=250 K##. How much work did the machine do?
Relevant Equations
First law of thermodynamics: ##\Delta U=Q-W##
Heat exchange: ##Q=C\cdot \Delta T##
This is how I solved part a) :
##Q_1=C\cdot (T_1-T_i)## This quantity is negative because object 1 loses heat. (positive for the machine)
##Q_2=C\cdot (T_2-T_i)## This one is positive because the object 2 absorbs heat.(negative for the machine)
Then the exchanged heat FOR THE MACHINE is ##Q=-Q_1-Q_2##
From the first law ##\Delta U=0 ⇒ Q=W ⇒ Q_2=-Q_1-W=4.44\cdot 10^5 J##
##T_2=\frac{Q_2}{C}+T_i=548 K##. Am I right?
For part b)... Do I have to use the relation ##\frac{Q_1}{Q_2}=\frac{T_1}{T_2}##?
I don't really know... Help me!

ValeForce46 said:
Do I have to use the relation ##\frac{Q_1}{Q_2}=\frac{T_1}{T_2}##?
Yes.

ValeForce46

## What is a cyclical thermal machine?

A cyclical thermal machine is a device that converts thermal energy into work through a cyclic process. It typically involves two objects with different temperatures exchanging heat, causing one object to expand and perform mechanical work.

## How does heat exchange occur in a cyclical thermal machine?

Heat exchange in a cyclical thermal machine occurs through a process called the Carnot cycle. This involves the objects being in contact with each other and exchanging heat until they reach thermal equilibrium, meaning they have the same temperature.

## What is the purpose of a cyclical thermal machine?

The purpose of a cyclical thermal machine is to convert thermal energy into mechanical work. This is useful in various industries, such as power plants, where heat is used to generate electricity.

## What is the efficiency of a cyclical thermal machine?

The efficiency of a cyclical thermal machine is determined by the Carnot efficiency formula, which is the ratio of the temperature difference between the two objects to the temperature of the hotter object. This means that the efficiency increases as the temperature difference increases.

## What factors affect the performance of a cyclical thermal machine?

The performance of a cyclical thermal machine can be affected by several factors, including the temperature difference between the two objects, the materials used, and the design and maintenance of the machine. Additionally, external factors such as heat loss and friction can also impact the performance.

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