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Q. No.Ten moles of oxygen gas (O₂) are heated at constant volume, causing the temperature to increase from 30°C to 40°C. Calculate the change in internal energy of the gas (in calories):
[Given: \(\mathrm{C}_p=7 \frac{\mathrm{Cal}}{\mathrm{~mol}-\mathrm{K}};~ \mathrm{R}=2 \frac{\mathrm{Cal}}{\mathrm{~mol}-\mathrm{K}}\)]
1. 400
2. 500
3. 600
4. 700
[Given: \(\mathrm{C}_p=7 \frac{\mathrm{Cal}}{\mathrm{~mol}-\mathrm{K}};~ \mathrm{R}=2 \frac{\mathrm{Cal}}{\mathrm{~mol}-\mathrm{K}}\)]
1. 400
2. 500
3. 600
4. 700
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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Calculate the enthalpy change for the combustion of octane if the heat capacity of a bomb calorimeter is 5 kJ K⁻¹ and the temperature of the calorimeter increases by 5°C during combustion in excess oxygen.
| 1. | 20 | 2. | 25 |
| 3. | 30 | 4. | 35 |
Subtopic: Enthalpy & Internal energy | Cp & Cv |
83%
Level 1: 80%+
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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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Calculate the molar heat capacity at constant volume, Cᵥ,ₘ, of a gaseous mixture containing 2 moles of a monoatomic gas and 6 moles of a diatomic gas.
Given:
For monoatomic gas, Cᵥ,ₘ = 3R/2
For diatomic gas, Cᵥ,ₘ = 5R/2
1. 9R/4
2. 9R/2
3. 3R
4. 4R
Subtopic: Cp & Cv |
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Calculate the enthalpy change during the combustion of coal if 2.4 g of pure carbon is burnt in excess oxygen in a bomb calorimeter at 298 K and 1 atm. The temperature of the calorimeter increases from 298 K to 300 K. The heat capacity of the bomb calorimeter is 20.0 kJ K⁻¹.
1. 600
2. 200
3. 284
4. 731
1. 600
2. 200
3. 284
4. 731
Subtopic: Cp & Cv |
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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. 6.0
2. 10
3. 2.0
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. 6.0
2. 10
3. 2.0
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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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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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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