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Q. No.Two monoatomic gases \(A,B\) are taken in two parts of a vessel having equal volumes \(V_0.\) The gases are at the same pressure \(P_0\) but at temperature of \(300~\text K\) and \(600~\text K.\) There is a partition between the parts of the vessel. The partition is removed, and the gases are allowed to mix. The vessel, as a whole, is insulated. The final temperature of the system is:
1. \(450~\text K\)
2. \(400~\text K\)
3. \(500~\text K\)
4. \(550~\text K\)
Subtopic: Work Done by a Gas |
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An ideal gas is taken from \(A\) to \(C\) through the process \(ABC\) and independently, from \(A\) to \(C\) through the process \(ADC\) – as shown on the indicator \((P\text -V)\) diagram. The work done in \(ABC\) is \(W_1\) and in \(ADC\) is \(W_2;\) the change in internal energy is \(\Delta U_1\) for process \(ABC,\) \(\Delta U_2\) for process \(ADC.\)
The temperatures at \(B\) and \(D\) are \(T_B\) and \(T_D,\) on the absolute scale. Then,
The temperatures at \(B\) and \(D\) are \(T_B\) and \(T_D,\) on the absolute scale. Then,
| 1. | \(T_B=T_D\) |
| 2. | \(T_B>T_D\) |
| 3. | \(T_B<T_D\) |
| 4. | the relationship between \(T_B,T_D\) depends on whether the gas is monoatomic or diatomic. |
Subtopic: Types of Processes |
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A monoatomic gas \((A)\) and a diatomic gas \((B)\) are taken in two separate identical containers at the same conditions of temperature and pressure.
The two gases \(A,B\) are allowed to expand adiabatically until their volumes are doubled. The final temperatures are \(\theta_A\) (for gas \(A\)) and \(\theta_B\) (for gas \(B\)). Then:
The two gases \(A,B\) are allowed to expand adiabatically until their volumes are doubled. The final temperatures are \(\theta_A\) (for gas \(A\)) and \(\theta_B\) (for gas \(B\)). Then:
| 1. | \(\theta_A=\theta_B\) |
| 2. | \(\theta_A<\theta_B\) |
| 3. | \(\theta_A>\theta_B\) |
| 4. | the relationship between \(\theta_A,\theta_B\) depends on the molecular weights of \(A\) and \(B\) |
Subtopic: Types of Processes |
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The same amount of heat is supplied to equimolar masses of hydrogen and helium, under constant pressure. The work done by the two gases, \(H_2\) and \(He,\) are \(W_1\) and \(W_2.\) Then:
| 1. | \(W_1>W_2\) |
| 2. | \(W_1<W_2\) |
| 3. | \(W_1=W_2\) |
| 4. | \(W_1\) and \(W_2\) cannot be compared unless the temperatures are known. |
Subtopic: Work Done by a Gas |
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One mole of an ideal monoatomic gas undergoes a slow reversible process in which its density \((\rho)\) is inversely proportional to its absolute temperature \((T).\)
The temperature of the gas increases from \(300~\text K\) to \(400~\text K.\) The work done by the gas during the process is:
(\(R\text:\) universal gas constant)
1. zero
2. \(-100~R\)
3. \(100~R\)
4. \(50~R\)
The temperature of the gas increases from \(300~\text K\) to \(400~\text K.\) The work done by the gas during the process is:
(\(R\text:\) universal gas constant)
1. zero
2. \(-100~R\)
3. \(100~R\)
4. \(50~R\)
Subtopic: Work Done by a Gas |
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Three different reversible processes involving ideal gases are shown on the volume-pressure diagram. Among the following given choices, one is correct. Which one?
| 1. | \(a-\)isothermal | 2. | \(c-\)isothermal |
| \(b-\)adiabatic, diatomic gas | \(b-\)adiabatic, diatomic gas | ||
| \(c-\)adiabatic, monoatomic gas | \(a-\)adiabatic, monoatomic gas | ||
| 3. | \(c-\)isothermal | 4. | \(a-\)isothermal |
| \(b-\)adiabatic, monoatomic gas | \(b-\)adiabatic, monoatomic gas | ||
| \(a-\)adiabatic, diatomic gas | \(c-\)adiabatic, diatomic gas |
Subtopic: Types of Processes |
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A monoatomic ideal gas undergoes a process given by the equation: \({\dfrac{pT}{V}}=\text{constant.}\) The molar specific heat capacity in the process equals:
| 1. | \({\dfrac{3}{2}}R\) | 2. | \({\dfrac{5}{2}}R\) |
| 3. | \({\dfrac{1}{2}}R\) | 4. | zero |
Subtopic: Molar Specific Heat |
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An ideal monoatomic gas undergoes a reversible process in which it doubles in volume, the equation of the process being: \(pVT=\text{constant}.\)
The internal energy of the gas at the beginning of the process equals \(U_0.\) The work done by the gas equals:
The internal energy of the gas at the beginning of the process equals \(U_0.\) The work done by the gas equals:
| 1. | \(U_0\) | 2. | \({\Large\frac23}U_0\) |
| 3. | \(U_0\mathrm{ln}2\) | 4. | \({\Large\frac23}U_0\mathrm{ln}2\) |
Subtopic: Work Done by a Gas |
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A Carnot engine operates between temperatures of \(27^\circ \mathrm C\) and \(127^\circ \mathrm C\) and performs \(2\) kJ of work. The amount of heat energy rejected is:
| 1. | \(4\) kJ | 2. | \(6\) kJ |
| 3. | \(8\) kJ | 4. | \(12\) kJ |
Subtopic: Carnot Engine |
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An ideal gas undergoes a thermodynamic process following the relation \(PT^2=\text{constant}\). Assuming symbols have their usual meaning, then the volume expansion coefficient of the gas is equal to:
1. \( \dfrac{2}{T}\)
2. \(\dfrac{3}{T}\)
3. \( \dfrac{1}{2 T} \)
4. \(\dfrac{1}{ T}\)
1. \( \dfrac{2}{T}\)
2. \(\dfrac{3}{T}\)
3. \( \dfrac{1}{2 T} \)
4. \(\dfrac{1}{ T}\)
Subtopic: Types of Processes |
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