Unit 9: Thermodynamics
Weightage : 15–18%
The figure shows a cylinder that has a movable piston and contains an ideal gas initially in state 1 at room temperature. The cylinder is sealed. Blocks of known mass can be added to or removed from the top of the piston. The gas is taken through the process represented by the graph of pressure \(P\) as a function of volume \(V\).
Which of the following actions could cause the gas to go through the process represented by the graph?
Correct Answer: \( \boxed{\mathrm{C}} \)
The graph shows that the pressure remains constant while the volume decreases. This is an isobaric process.
According to the ideal gas law,
\( PV=nRT. \)
Since the amount of gas and the pressure remain constant,
\( \frac{V}{T}=\text{constant}. \)
Cooling the gas by placing the cylinder on a block of ice decreases its temperature. With the pressure held constant by the fixed mass on the piston, the piston moves downward and the gas volume decreases.
Adding mass to the piston would increase the pressure, so the process would not be horizontal on the \(P\)-\(V\) graph. Heating the gas at constant pressure would increase the volume rather than decrease it.
Therefore, the correct answer is (C).
An ideal gas in a closed container initially has volume \(V\), pressure \(P\), and Kelvin temperature \(T\). If the temperature is changed to \(3T\), which of the following pairs of pressure and volume values is possible?
Correct Answer: \( \boxed{\mathrm{A}} \)
For a fixed amount of an ideal gas,
\( PV=nRT. \)
Since the amount of gas (\(n\)) and the gas constant (\(R\)) remain constant,
\( PV\propto T. \)
If the temperature increases from \(T\) to \(3T\), then the product \(PV\) must also increase by a factor of \(3\):
\( P’V’=3PV. \)
Checking the options:
(A) \( (3P)(V)=3PV\) ✔
(B) \( (3P)(3V)=9PV\) ✘
(C) \( P\left(\dfrac{V}{3}\right)=\dfrac{PV}{3}\) ✘
(D) \( \left(\dfrac{P}{3}\right)V=\dfrac{PV}{3}\) ✘
Therefore, the only possible pair of pressure and volume values is \(3P\) and \(V\).
Therefore, the correct answer is (A).
Which graph best represents the relationship between pressure and volume for an ideal confined gas at constant temperature?
I 
II 
III 
IV 
Correct Answer: \( \boxed{\mathrm{C}} \)
For a fixed amount of an ideal gas at constant temperature (an isothermal process), the ideal gas law gives
\( PV=nRT=\text{constant}. \)
Therefore,
\( P=\dfrac{\text{constant}}{V}. \)
This means that pressure is inversely proportional to volume, a relationship known as Boyle’s Law. As the volume increases, the pressure decreases, producing a rectangular hyperbola.
Among the four graphs, only Graph III shows this inverse relationship between pressure and volume.
Therefore, the correct answer is (C).
