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Questions and Answers
What is the internal energy of a system defined as?
What is the internal energy of a system defined as?
- The sum total of kinetic and potential energy of the molecules. (correct)
- The sum total of thermal energy only.
- The sum total of only kinetic energy of the molecules.
- The sum total of temperature and pressure of the system.
What does the area under the curve ab in an indicator diagram represent?
What does the area under the curve ab in an indicator diagram represent?
- The change in temperature of the system.
- The total work done by the system.
- The pressure of the system.
- The change in internal energy ($ΔU$). (correct)
How can the work done (W) by the system be determined from the indicator diagram?
How can the work done (W) by the system be determined from the indicator diagram?
- By integrating pressure over volume. (correct)
- By summing the forces acting on the system.
- By measuring the height of the curve.
- By calculating the temperature change.
What is the calculated work done (W) when $P = 0.01 imes 10^3 ext{ N/m}^2$ and $ΔV = 10 ext{ m}^3$?
What is the calculated work done (W) when $P = 0.01 imes 10^3 ext{ N/m}^2$ and $ΔV = 10 ext{ m}^3$?
Under which condition is the work done (W) equal to zero?
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
-
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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