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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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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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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\(10\) mole of oxygen is heated at constant volume from \(30^{\circ}\text{C}\) to \(40^{\circ}\text{C}\). The change in the internal energy of the gas is: (in cal)
The molecular specific heat of oxygen at constant pressure, \(C_P=7\) cal./mol °C and \(R=2\) cal./mol °C.)
1. \(300\)
2. \(400\)
3. \(500\)
4. \(600\)
The molecular specific heat of oxygen at constant pressure, \(C_P=7\) cal./mol °C and \(R=2\) cal./mol °C.)
1. \(300\)
2. \(400\)
3. \(500\)
4. \(600\)
Subtopic: Molar Specific Heat |
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Level 1: 80%+
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When \(300~\text{J}\) of heat given to an ideal gas with \(C_p= \dfrac{7}{2}R\) its temperature raises from \(20^\circ\text{C}\) to \(50^\circ \text{C}\) keeping its volume constant. The mass of the gas is (approximately): (in g) \((R=8.314~ \text{J/mol.K})\)
1. \(.48\) moles
2. \(.50\) moles
3. \(.55\) moles
4. \(.60\) moles
1. \(.48\) moles
2. \(.50\) moles
3. \(.55\) moles
4. \(.60\) moles
Subtopic: Molar Specific Heat |
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Level 1: 80%+
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Water falls from a height of \(200~\text{m}\) into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool. (Take \(g = 10~\text{m/s}^2 , \) specific heat of water \(= 4200~\text{J/(kg K)} \))
1. \(0.23~\text K\)
2. \(0.36~ \text K\)
3. \(0.14~ \text K\)
4. \(0.48 ~\text K\)
1. \(0.23~\text K\)
2. \(0.36~ \text K\)
3. \(0.14~ \text K\)
4. \(0.48 ~\text K\)
Subtopic: Molar Specific Heat |
Level 4: Below 35%
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Match the List-I with List-II.
Choose the correct answer from the options given below:
| List-I | List-II | ||
| \(\mathrm{A}.\) | Triatomic rigid gas | \(\mathrm{I}.\) | \(\dfrac{C_p}{C_v}=\dfrac{5}{3}\) |
| \(\mathrm{B}.\) | Diatomic non-rigid gas | \(\mathrm{II}.\) | \(\dfrac{C_p}{C_v}=\dfrac{7}{5}\) |
| \(\mathrm{C}.\) | Monoatomic gas | \(\mathrm{III}.\) | \(\dfrac{C_p}{C_v}=\dfrac{4}{3}\) |
| \(\mathrm{D}.\) | Diatomic rigid gas | \(\mathrm{IV}.\) | \(\dfrac{C_p}{C_v}=\dfrac{9}{7}\) |
| 1. | \(\mathrm{A\text-III, B\text-II, C\text-IV, D\text-I}\) |
| 2. | \(\mathrm{A\text-II, B\text-IV, C\text-I, D\text-II}\) |
| 3. | \(\mathrm{A\text-IV, B\text-II, C\text-III, D\text-I}\) |
| 4. | \(\mathrm{A\text-III, B\text-IV, C\text-I, D\text-II}\) |
Subtopic: Molar Specific Heat |
Level 4: Below 35%
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\(\gamma_A\) is the specific heat ratio of monoatomic gas \(A\) having \(3\) translational degrees of freedom. \(\gamma_B\) is the specific heat ratio of polyatomic gas \(B\) having \(3\) translational, \(3\) rotational degrees of freedom and \(1\) vibrational mode. If \(\dfrac{\gamma_A}{\gamma_B}=\left(1+\dfrac{1}{n}\right) \), then the value of \(n\) is:
1. \(3\)
2. \(4\)
3. \(5\)
4. \(6\)
1. \(3\)
2. \(4\)
3. \(5\)
4. \(6\)
Subtopic: Molar Specific Heat |
Level 4: Below 35%
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The temperature of \(1~\text{mole}\) of an ideal monoatomic gas is increased by \(50^\circ \text{C} \) at constant pressure. The total heat added and the change in internal energy are \(E_1 \) and \(E_2\), respectively. If \(\dfrac{E_1}{E_2}=\dfrac{x}{9}\) then the value of \(x\) is:
1. \(60\)
2. \(30\)
3. \(15\)
4. \(18\)
1. \(60\)
2. \(30\)
3. \(15\)
4. \(18\)
Subtopic: Molar Specific Heat |
100%
Level 1: 80%+
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The specific heat at constant pressure of a real gas obeying \(\mathrm{PV}^2=\mathrm{RT}\) equation is:
1. \(\frac{R}{3}+C_v\)
2. \(R\)
3. \(C_v+R\)
4. \(C_v+R / 2 V\)
1. \(\frac{R}{3}+C_v\)
2. \(R\)
3. \(C_v+R\)
4. \(C_v+R / 2 V\)
Subtopic: Molar Specific Heat |
Level 3: 35%-60%
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