# How Is Work Calculated in a Thermodynamic Process with Constant T2/V Ratio?

• DottZakapa
In summary, a bi-atomic ideal gas with n moles is initially at temperature TA and volume VA. When an amount M of methane is burned, the temperature is doubled while the volume is expanded to maintain a constant ratio between the two. Assuming no heat is wasted, the work done during this transformation can be calculated using the relation W=∫ p⋅dV=2nRTA, where p is the pressure expressed as a function of n, TA, VA, and V. The initial pressure pA can be calculated using the ideal gas law, and the pressure at volume V can be calculated using the same law with the new temperature and volume values.
DottZakapa
A volume VA contains n mole of a bi-atomic ideal gas, initially at temperature TA. Burning an amount M of methane, whose calorific power P (produced heat per unit mass while burning) is 13271 [kcal/kg], the temperature is slowly doubled, simultaneously expanding the volume in order to maintain the ratio (T2 / V) constant. Assuming that no heat is wasted in the environment.
DATA:
n= 0.3 [mole]; R= 0.082 [litre*atm/(mole*K)] ;
VA=9 [litre] ; TA=300 [K]; 1 [cal]=4.18[J]]

Following there is what I've solved so far:
PA=(nRTA)/ VA

TB= 2TA

VB=(TB2⋅VA)/ TA2= 4VA

PB=(nR2TA)/ 4VA

Considering that pressure and temperature aren't constant during the transformation, I'm not sure which value instead of pressure I have to insert in the integral in order to evaluate the work during the transformation.

W=∫ p⋅dV

I guess that I shall use this relation :

T2 / V = TA2 / VA

The solution to this is :

W=∫ p⋅dV=2nRTA

but I don't get how.
Could somebody help me with this?
Thanks

Last edited:
How are T, V, TA, and VA related?

In terms of TA, VA, and n, what is the initial pressure pA?

What is the pressure when the volume is V?

Chet

Chestermiller said:
How are T, V, TA, and VA related?

In terms of TA, VA, and n, what is the initial pressure pA?

What is the pressure when the volume is V?

Chet
I've edited the template

Express p as a function of n, TA, VA and V. Then integrate.

Chet

## 1. What is thermodynamics?

Thermodynamics is a branch of physics that deals with the relationships between heat, work, and energy. It studies how energy is transferred and transformed in physical systems, and how these processes affect the properties of matter.

## 2. How does thermodynamics relate to finding work?

Thermodynamics plays a crucial role in understanding and predicting the amount of work that can be obtained from a given system. The laws of thermodynamics dictate the maximum amount of work that can be extracted from a system, and this information is essential in finding work in various processes and industries.

## 3. What are the laws of thermodynamics?

The laws of thermodynamics are fundamental principles that govern the behavior of energy in physical systems. The first law states that energy cannot be created or destroyed, only transferred or transformed. The second law states that the total entropy of a closed system will never decrease over time, and the third law states that the entropy of a pure, perfect crystal at absolute zero temperature is zero.

## 4. How is thermodynamics used in industry?

Thermodynamics is used in a wide range of industries, including power generation, chemical processing, and refrigeration. It is used to design and optimize systems to maximize energy efficiency and minimize waste. It is also used in the development of new materials and processes.

## 5. What are some common applications of thermodynamics?

Some common applications of thermodynamics include engines, refrigerators, air conditioners, and power plants. It is also used in the study of weather and climate, as well as in understanding the behavior of materials and chemical reactions. Thermodynamics has a wide range of applications and is an essential tool in many fields of science and engineering.

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