Respuesta :
The change in internal energy of a gold bar is [tex]\boxed{{\text{322 J}}}[/tex]
Further explanation:
Thermodynamics:
It is branch of chemistry that is related to heat temperature and connection with work is known as thermodynamics it has wide uses in pyrometallurgy, gas phase reaction gas solid reaction and ATP generation and many more.
First law of Thermodynamics:
It is based on law of energy conservation that states total energy of system remains constant. According to this law, internal energy change is determined by sum of work done on the system and heat supplied. Its mathematical expression is as follows:
[tex]\Delta {\text{U}}={\text{q}}+{\text{W}}[/tex] …… (1)
Here,
[tex]\Delta{\text{U}}[/tex] is the change in internal energy of the system.
q is the heat supplied to the system.
W is the work done on the system.
The formula to calculate the work done is as follows:
[tex]{\text{W}}={\text{P}}\Delta{\text{V}}[/tex] …… (2)
Here,
W is the work done.
P is the pressure on the system.
[tex]\Delta{\text{V}}[/tex] is the change in the volume of the system.
It is given that the volume of the gold bar remains constant. This implies [tex]\Delta{\text{V}}[/tex] to be zero.
Substitute 0 for [tex]\Delta{\text{V}}[/tex] in equation (2) to calculate the work done on the gold bar.
[tex]\begin{aligned}{\text{W}}&={\text{P}}\left( 0 \right)\\&=0\\\end{aligned}[/tex]
The value of q is 322 J.
The value of W is 0.
Substitute these values in equation (1) to calculate the change in the internal energy of the gold bar.
[tex]\begin{gathered}\Delta{\text{U}}={\text{322 J}}+0\\={\text{322 J}}\\\end{gathered}[/tex]
So the change in internal energy of gold bar is 322 J.
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Answer details:
Grade: Senior School
Subject: Chemistry
Chapter: Thermodynamics
Keywords: internal energy, heat, work, q, W, P, 322 J, 0, thermodynamics, first law of thermodynamics, law of conservation of energy, total energy, isolated system, volume, constant.
Assuming the volume of the gold bar remains constant, the change in internal energy of this system is equal to 322 Joules.
Given the following data:
- Mass of gold bar = 100.0 grams
- Initial temperature = 25°C
- Final temperature = 50°C
- Quantity of heat energy = 322 Joules
To calculate the change in internal energy of the system, assuming the volume of the gold bar remains constant:
A system in which the volume remains constant while other quantities vary is referred to as an isochoric system and the work done by this system is always equal to zero (0).
This ultimately implies that, the quantity of heat energy that is transferred to an isochoric system externally would be absorbed as internal energy.
Note: The First Law of Thermodynamics is used to calculate the change in internal energy of a system.
Mathematically, the First Law of Thermodynamics is given by the formula:
[tex]\Delta U = Q - W[/tex]
Where;
- [tex]\Delta U[/tex] is the change in internal energy.
- Q is the quantity of heat absorbed.
- W is the work done.
Substituting the parameters into the formula, we have;
[tex]\Delta U = 322 - 0\\\\\Delta U = 322\;Joules[/tex]
Change in internal energy = 322 Joules.
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