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Questions and Answers
What is the internal energy of a system defined as?
What does the area under the curve ab in an indicator diagram represent?
How can the work done (W) by the system be determined from the indicator diagram?
What is the calculated work done (W) when $P = 0.01 imes 10^3 ext{ N/m}^2$ and $ΔV = 10 ext{ m}^3$?
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Under which condition is the work done (W) equal to zero?
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Study Notes
Internal Energy
- The sum of kinetic and potential energy of the molecules within a system is called its internal energy
- Represented by the symbol U
- Internal energy varies directly with temperature ($U \propto T$)
Indicator Diagram
- A visual representation of pressure changes against volume is called an indicator diagram.
- The line depicting this variation is known as the indicator diagram.
Significance
- The area under the curve ab in the indicator diagram represents the change in internal energy ($ΔU$).
- Mathematically, the area under the curve ab is equal to $\int{PdV} = \Delta U$.
- The area under the curve AD represents the work done (W) by the system.
- The work done can be calculated from the indicator diagram by determining the area underneath it.
- Mathematically, this is represented as: $W = \int_{AB} PdV$.
Example Calculation
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Given:
- $P = 0.01 \times 10^3 \text{ N/m}^2$
- $ΔV = 10 \text{ m}^3$
-
$W = \int_{AB} P dV = 10^{-2} (N m^{-2}) \times 10 \times 10^{-3} m^3$
-
$W = 10^{-2} \times 10^{-3} \times 10 = 10^{-2} \text{ Joules} = 10^{-1}\text{ J} = 0.1 \text{ J} $
Case 2
- If $AB = 0$, the work done is $W = 0$.
- Alternatively, if $V = const$. then $dv = 0$, meaning $dw = 0$, and therefore $w = 0$.
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Description
Explore the concepts of internal energy and indicator diagrams in thermodynamics. This quiz covers the relationship between internal energy and temperature, along with the significance of area under the curve in indicator diagrams. Test your understanding with example calculations and theoretical questions.
