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Q. No.A mixture contains one mole of a monoatomic gas and one mole of a diatomic gas. What is the ratio of the heat capacities at constant volume (\(C_V\)) to the heat capacities at constant pressure (\(C_P\)) for the mixture\(\left(\text { i.e. } \frac{C_v}{C_P}\right)\)?
| 1. | \(\dfrac{2}{3}\) | 2. | \(\dfrac{7}{5}\) |
| 3. | \(\dfrac{5}{7}\) | 4. | \(\dfrac{3}{5}\) |
Subtopic: Cp & Cv |
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A container of fixed volume filled with an ideal gas which have \(\frac{C_P}{C_V}=1.4,\) is moving with velocity 'v' and then suddenly stopped. If no heat loss is observed, then the final increase in temperature is: (M=Molar mass of gas).
1. \(\frac{Mv^2}{7R}\)
2. \(\frac{2Mv^2}{7R}\)
3. \(\frac{2Mv^2}{5R}\)
4. \(\frac{Mv^2}{5R}\)
1. \(\frac{Mv^2}{7R}\)
2. \(\frac{2Mv^2}{7R}\)
3. \(\frac{2Mv^2}{5R}\)
4. \(\frac{Mv^2}{5R}\)
Subtopic: Cp & Cv |
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Level 3: 35%-60%
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We have a mixture of gases having \(2\) moles of monoatomic gas \(\left(C_{v, m}=\frac{3 R}{2}\right)\)and \(6\) moles of diatomic gas \(\left(\text{C}_{\text{v, m}}=\frac{5 R}{2}\right)\). Find out molar heat capacity \((\text{C}_{\text{vm}})\) of the mixture.
1. \(\frac{9 R}{4}\)
2. \(\frac{9 R}{2}\)
3. 3R
4. 4R
1. \(\frac{9 R}{4}\)
2. \(\frac{9 R}{2}\)
3. 3R
4. 4R
Subtopic: Cp & Cv |
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\(\mathrm{2.4~g}\) Coal is burnt in a bomb calorimeter in excess of oxygen at \(\mathrm{298~K~and~1~atm}\). The temperature of the calorimeter rises from \(\mathrm{298~K}\) to \(\mathrm{300~K}.\) The enthalpy change during the combustion of coal is \(-\mathrm{x}~ \mathrm{kJ} ~\mathrm{mol}{ }^{-1} \text {. }\) Find the value of \(\mathrm{x}\):
[Note: Assume coal to be pure carbon]
[Given : Heat capacity of bomb calorimeter is \(\mathrm{20.0~kJ~K^{-1}.}\) ]
1. 600
2. 200
3. 284
4. 731
[Note: Assume coal to be pure carbon]
[Given : Heat capacity of bomb calorimeter is \(\mathrm{20.0~kJ~K^{-1}.}\) ]
1. 600
2. 200
3. 284
4. 731
Subtopic: Cp & Cv |
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Level 2: 60%+
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The molar heat capacity for an ideal gas at constant pressure is \(20.785 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1} \text {. }\)
If the change in internal energy is \(5000~ \text J\) upon heating it from \( 300~\text K\) to \(500~ \text K\), then what is the number of moles of the gas at constant volume ?
(Given : \(\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\))
1. 6
2. 10
3. 2
4. 20
If the change in internal energy is \(5000~ \text J\) upon heating it from \( 300~\text K\) to \(500~ \text K\), then what is the number of moles of the gas at constant volume ?
(Given : \(\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\))
1. 6
2. 10
3. 2
4. 20
Subtopic: Cp & Cv |
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When 600 mL of 0.2 M \(\mathrm{HNO}_3\) is mixed with 400 mL of 0.1 M \(\text {NaOH}\) solution in a flask, the rise in the temperature of the flask is \(x \times 10^{-2}~{ }^{\circ} \text{C}\). Find the value of \(x\). (Neglect the heat capacity of flask):
(Given: Enthalpy of neutralisation = \(57 \mathrm{~kJ} \mathrm{~mol}^{-1}\) and Specific heat of water = \(4.2 \mathrm{JK}^{-1} \mathrm{~g}^{-1}\))
1. \(34\)
2. \(67\)
3. \(54\)
4. \(18\)
(Given: Enthalpy of neutralisation = \(57 \mathrm{~kJ} \mathrm{~mol}^{-1}\) and Specific heat of water = \(4.2 \mathrm{JK}^{-1} \mathrm{~g}^{-1}\))
1. \(34\)
2. \(67\)
3. \(54\)
4. \(18\)
Subtopic: Cp & Cv |
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The change in internal energy is found to be 5000 J, when 4 mole of an ideal gas is heated from 300 K to 500 K at constant volume. What is the molar heat capacity at constant volume?
1. 3.50
2. 6.25
3. 8.15
4. 9.80
1. 3.50
2. 6.25
3. 8.15
4. 9.80
Subtopic: Cp & Cv |
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Ice at –5°C is heated to convert into vapour with temperature of 110°C at atmospheric pressure. The entropy change associated with this process can be obtained from which of the following?
[Where: \(T_f\) is melting point and \(T_b\) is boiling point]
1. \(\int_{268 \mathrm{~K}}^{383 \mathrm{~K}} \mathrm{C}_{\mathrm{p}} \mathrm{dT}+\frac{\Delta \mathrm{H}_{\text {melting }}}{273}+\frac{\Delta \mathrm{H}_{\text {boiling }}}{373}\)
2. \(\int_{268 \mathrm{~K}}^{273 \mathrm{~K}} \frac{\mathrm{C}_{\mathrm{p}, \mathrm{~m}}}{\mathrm{~T}} \mathrm{dT}+\frac{\Delta \mathrm{H}_{\mathrm{m}}, \text { fusion }}{\mathrm{T}_{\mathrm{f}}}+\int_{273 \mathrm{~K}}^{373 \mathrm{~K}} \frac{\mathrm{C}_{\mathrm{p}, \mathrm{~m}} \mathrm{dT}}{\mathrm{~T}}+ \frac{\Delta \mathrm{H}_{\mathrm{m}, \text { vaporisation }}}{\mathrm{T}_{\mathrm{b}}}\)\(+\int_{373 \mathrm{~K}}^{383 \mathrm{~K}} \frac{\mathrm{C}_{\mathrm{p}, \mathrm{~m}} \mathrm{dT}}{\mathrm{~T}}\)
3. \(\int_{268 \mathrm{~K}}^{383 \mathrm{~K}} \mathrm{C}_{\mathrm{p}} \mathrm{dT}+\frac{\mathrm{q}_{\mathrm{rev}}}{\mathrm{~T}}\)
4. \(\begin{aligned} & \int_{268 \mathrm{~K}}^{273 \mathrm{~K}} \mathrm{C}_{\mathrm{p}, \mathrm{~m}} \mathrm{dT} +\int_{273 \mathrm{~K}}^{373 \mathrm{~K}} \mathrm{C}_{\mathrm{p}, \mathrm{~m}} \mathrm{dT}+\int_{373 \mathrm{~K}}^{383 \mathrm{~K}} \mathrm{C}_{\mathrm{p}, \mathrm{~m}} \mathrm{dT} \end{aligned}\)
[Where: \(T_f\) is melting point and \(T_b\) is boiling point]
1. \(\int_{268 \mathrm{~K}}^{383 \mathrm{~K}} \mathrm{C}_{\mathrm{p}} \mathrm{dT}+\frac{\Delta \mathrm{H}_{\text {melting }}}{273}+\frac{\Delta \mathrm{H}_{\text {boiling }}}{373}\)
2. \(\int_{268 \mathrm{~K}}^{273 \mathrm{~K}} \frac{\mathrm{C}_{\mathrm{p}, \mathrm{~m}}}{\mathrm{~T}} \mathrm{dT}+\frac{\Delta \mathrm{H}_{\mathrm{m}}, \text { fusion }}{\mathrm{T}_{\mathrm{f}}}+\int_{273 \mathrm{~K}}^{373 \mathrm{~K}} \frac{\mathrm{C}_{\mathrm{p}, \mathrm{~m}} \mathrm{dT}}{\mathrm{~T}}+ \frac{\Delta \mathrm{H}_{\mathrm{m}, \text { vaporisation }}}{\mathrm{T}_{\mathrm{b}}}\)\(+\int_{373 \mathrm{~K}}^{383 \mathrm{~K}} \frac{\mathrm{C}_{\mathrm{p}, \mathrm{~m}} \mathrm{dT}}{\mathrm{~T}}\)
3. \(\int_{268 \mathrm{~K}}^{383 \mathrm{~K}} \mathrm{C}_{\mathrm{p}} \mathrm{dT}+\frac{\mathrm{q}_{\mathrm{rev}}}{\mathrm{~T}}\)
4. \(\begin{aligned} & \int_{268 \mathrm{~K}}^{273 \mathrm{~K}} \mathrm{C}_{\mathrm{p}, \mathrm{~m}} \mathrm{dT} +\int_{273 \mathrm{~K}}^{373 \mathrm{~K}} \mathrm{C}_{\mathrm{p}, \mathrm{~m}} \mathrm{dT}+\int_{373 \mathrm{~K}}^{383 \mathrm{~K}} \mathrm{C}_{\mathrm{p}, \mathrm{~m}} \mathrm{dT} \end{aligned}\)
Subtopic: Cp & Cv | Spontaneity & Entropy |
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The heat capacity of a bomb calorimeter is \(5 \mathrm{~kJ} / \mathrm{K}.\) When combustion of octane takes place in presence of excess \(\mathrm{O}_2\), the temperature rises by \(5^{\circ} \mathrm{C}.\) The value of \(\Delta \mathrm{H}_{\text {combustion }}\) in \(\mathrm{kJ }\) is:
| 1. | 20 | 2. | 25 |
| 3. | 30 | 4. | 35 |
Subtopic: Enthalpy & Internal energy | Cp & Cv |
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