The initial pressure and volume of a gas are $$P$$ and $$V$$, respectively. First, it is expanded isothermally to volume $$4V$$ and then compressed adiabatically to volume $$V$$. The final pressure of the gas will be: [Given: $$\gamma = 1.5$$] 1. $$P$$ 2. $$2P$$ 3. $$4P$$ 4. $$8P$$

Subtopic:  Types of Processes |
74%
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If n moles of an ideal gas is heated at a constant pressure from 50°C to 100°C, the increase in the internal energy of the gas will be: $$\left(\frac{C_{p}}{C_{v}} = \gamma\ and\ R = gas\ constant\right)$$

 1 $$\frac{50 nR}{\gamma - 1}$$ 2 $$\frac{100 nR}{\gamma - 1}$$ 3 $$\frac{50 nγR}{\gamma - 1}$$ 4 $$\frac{25 nγR}{\gamma - 1}$$
Subtopic:  Molar Specific Heat |
81%
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A monoatomic ideal gas, initially at temperature $$T_1$$, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $$T_2$$ by releasing the piston suddenly. If $$L_1$$ and $$L_2$$ are the lengths of the gas column before and after expansion, respectively, then $$\frac{T_1}{T_2}$$ is given by:
1. $$\left(\frac{L_1}{L_2}\right)^{\frac{2}{3}}$$
2. $$\frac{L_1}{L_2}$$
3. $$\frac{L_2}{L_1}$$
4. $$\left(\frac{L_2}{L_1}\right)^{\frac{2}{3}}$$

Subtopic:  Types of Processes |
70%
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An ideal heat engine working between temperatures T1 and T2 has an efficiency η. The new efficiency if both the source and sink temperatures are doubled will be:
1. $\frac{\eta }{2}$
2. η
3. 2η
4. 3η

Subtopic:  Carnot Engine |
88%
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The latent heat of vaporisation of water is $$2240~\text{J/gm}$$. If the work done in the process of expansion of $$1~\text{g}$$ is $$168~\text{J}$$, then the increase in internal energy is:
1. $$2408~\text{J}$$
2. $$2240~\text{J}$$
3. $$2072~\text{J}$$
4. $$1904~\text{J}$$

Subtopic:  First Law of Thermodynamics |
82%
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The figure below shows two paths that may be taken by a gas to go from state A to state C. In process AB, $$400~\text{J}$$ of heat is added to the system and in process BC, $$100~\text{J}$$ of heat is added to the system. The heat absorbed by the system in the process AC will be:

 1 $$380~\text{J}$$ 2 $$500~\text{J}$$ 3 $$460~\text{J}$$ 4 $$300~\text{J}$$
Subtopic:  First Law of Thermodynamics |
64%
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The first law of thermodynamics is based on:

 1 the concept of temperature. 2 the concept of conservation of energy. 3 the concept of working of heat engine. 4 the concept of entropy.

Subtopic:  First Law of Thermodynamics |
92%
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The efficiency of an ideal heat engine is less than 100% because of:

 1 the presence of friction. 2 the leakage of heat energy. 3 unavailability of the sink at zero kelvin. 4 All of these

Subtopic:  Carnot Engine |
83%
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Work done during the given cycle is:

1. 4${P}_{0}{V}_{0}$

2. 2${P}_{0}{V}_{0}$

3. $\frac{1}{2}$${P}_{0}{V}_{0}$

4. ${P}_{0}{V}_{0}$

Subtopic:  Work Done by a Gas |
78%
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An ideal gas goes from A to B via two processes, l and ll, as shown. If $∆{\mathrm{U}}_{1}$ and $∆{\mathrm{U}}_{2}$ are the changes in internal energies in processes I and II, respectively, then ($$P:$$ pressure, $$V:$$ volume)

 1 ∆U1 > ∆U2 2 ∆U1 < ∆U2 3 ∆U1 = ∆U2 4 ∆U1 ≤ ∆U2
Subtopic:  Molar Specific Heat |
87%
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