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Q. No.\(5\) moles of unknown gas is heated at constant volume from \(10^\circ\text{C}\) to \(20^\circ\text{C}.\) The molar specific heat of this gas at constant pressure \(c_p=8~\text{cal/mol}^{\circ}\text{C}\) and \(R=8.36~ \text{J/mol}.^{\circ}\text{C} .\) The change in the internal energy of the gas is:
1. \(100~\text{cal}\)
2. \(200~\text{cal}\)
3. \(300~\text{cal}\)
4. \(400~\text{cal}\)
1. \(100~\text{cal}\)
2. \(200~\text{cal}\)
3. \(300~\text{cal}\)
4. \(400~\text{cal}\)
Subtopic: Molar Specific Heat |
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Level 2: 60%+
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A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same \(P,V,T.\) Heating is started from left side until pressure changes to \(\dfrac{27P}{8}.\) If initial volume of each compartment was \(9\) litres then the final volume in right-hand side compartment is: (in L) (for this ideal gas \(C_P / C_V=1.5\))
1. \(3\)
2. \(4\)
3. \(14\)
4. \(9\)
1. \(3\)
2. \(4\)
3. \(14\)
4. \(9\)
Subtopic: Types of Processes |
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Level 2: 60%+
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If \(2\) mole of an ideal monoatomic gas at temperature \(T,\) is mixed with \(6 \) mole of another ideal monoatomic gas at temperature \(2T\) then the temperature of mixture is:
1. \(\dfrac{5}{2} T \)
2. \(\dfrac{5}{4} T \)
3. \(\dfrac{7}{2} T \)
4. \(\dfrac{7}{4} T\)
1. \(\dfrac{5}{2} T \)
2. \(\dfrac{5}{4} T \)
3. \(\dfrac{7}{2} T \)
4. \(\dfrac{7}{4} T\)
Subtopic: Molar Specific Heat |
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Level 2: 60%+
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A certain gas is isothermally compressed to\(\left(\dfrac{1}{3}\right)^{\text {rd }}\) of its initial volume \((V_0=3 ~\text{litre})\) by applying required pressure. If the bulk modulus of the gas is\(3 \times 10^5 ~\text{N/m}^2,\) the magnitude of work done on the gas is: (in J)
1. \(750\)
2. \(760\)
3. \(706\)
4. \(989\)
1. \(750\)
2. \(760\)
3. \(706\)
4. \(989\)
Subtopic: Work Done by a Gas |
Level 4: Below 35%
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A vessel contains \(0.15~\text{m}^3\) of gas at pressure \(8\) bar and temperature \(140^\circ\text{C}\) with \(C_P=3R\) and \(C_V=2R\). It is expanded adiabatically till pressure falls to \(1\) bar. The work done during this process is: (in kJ) (\(R\) is gas constant)
1. \(70\)
2. \(80\)
3. \(120\)
4. \(200\)
1. \(70\)
2. \(80\)
3. \(120\)
4. \(200\)
Subtopic: Types of Processes |
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Level 2: 60%+
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Given below are two statements:
Choose the correct answer from the options given below:
| Assertion (A): | Change in internal energy of a system containing \(n\) mole of ideal gas can be written as \(\Delta {U}=n {C}_v\left(T_{{f}}-T_i\right)=\dfrac{n R}{\gamma-1}\left(T_{{f}}-T_i\right)\) , where \(\gamma=\dfrac{C_p}{C_v}, T_i=\) initial temperature, \(T_f\) = final temperature. |
| Reason (R): | Relation between degree of freedom \(f\) and \(\gamma~\left(\gamma =C_p / C_v\right) \text { is }\)\(\left(\gamma=1+\dfrac{2}{f}\right)~\) |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Types of Processes |
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Level 1: 80%+
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Consider the following statements:
Choose the correct combination of statements from the options given below:
1. \(\mathrm{C,D~\text{and}~E~\text{Only}}\)
2. \(\mathrm{A,B~\text{and}~C~\text{Only}}\)
3. \(\mathrm{A,B~\text{and}~D~\text{Only}}\)
4. \(\mathrm{B,C~\text{and}~D~\text{Only}}\)
| \(\mathrm{A.}\) | Zeroth law of thermodynamics gives concept of temperature |
| \(\mathrm{B.}\) | First law of thermodynamics gives concept of internal energy |
| \(\mathrm{C.}\) | In isothermal expansion of ideal gas, \(\Delta Q \neq \Delta W\) |
| \(\mathrm{D.}\) | Product of intensive and extensive variables is extensive |
| \(\mathrm{E.}\) | The ratio of any extensive variable to mass will be an extensive variable |
1. \(\mathrm{C,D~\text{and}~E~\text{Only}}\)
2. \(\mathrm{A,B~\text{and}~C~\text{Only}}\)
3. \(\mathrm{A,B~\text{and}~D~\text{Only}}\)
4. \(\mathrm{B,C~\text{and}~D~\text{Only}}\)
Subtopic: First Law of Thermodynamics |
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Level 1: 80%+
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An ideal gas at pressure \(P\) and temperature \(T\) is expanding such that \(PT^3= \text{constant}\). The coefficient of volume expansion of the gas is:
1. \(\dfrac{2}{T}\)
2. \(\dfrac{1}{T}\)
3. \(\dfrac{4}{T}\)
4. \(\dfrac{3}{T}\)
1. \(\dfrac{2}{T}\)
2. \(\dfrac{1}{T}\)
3. \(\dfrac{4}{T}\)
4. \(\dfrac{3}{T}\)
Subtopic: Types of Processes |
Level 4: Below 35%
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The heat extracted out of \(x\) gram of water initially at \(50^{\circ} \text{C}\) \(0^{\circ} \text{C}\)
(Take latent heat of water \(2256~ \text{kJ/kg} . \text{K} \text {, }\)specific heat capacity of water \(4200 ~\text{J} / \text{kg} \cdot \text{K}\))
1. \(850\)
2. \(922\)
3. \(740\)
4. \(600\)
(Take latent heat of water \(2256~ \text{kJ/kg} . \text{K} \text {, }\)specific heat capacity of water \(4200 ~\text{J} / \text{kg} \cdot \text{K}\))
1. \(850\)
2. \(922\)
3. \(740\)
4. \(600\)
Subtopic: Molar Specific Heat |
Level 4: Below 35%
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One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system. The cross-section area of the cylinder is \(4~\text{cm}^2\). The gas is heated slowly to raise the temperature by \(1.2^{\circ} \text{C}\)
(Atmospheric pressure\(=100~\text{kPa}, R=8.3~\text{J/mol K} \)
1. \(24.8\)
2. \(25\)
3. \(15.04\)
4. \(29.98\)
(Atmospheric pressure
1. \(24.8\)
2. \(25\)
3. \(15.04\)
4. \(29.98\)
Subtopic: First Law of Thermodynamics |
Level 4: Below 35%
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