Q. No.An ideal gas goes from \(A\) to \(B\) via two processes, \(\mathrm{I}\) and \(\mathrm{II},\) as shown. If \(\Delta U_1\) and \(\Delta U_2\) are the changes in internal energies in processes \(\mathrm{I}\) and \(\mathrm{II},\) respectively, (\(P:\) pressure, \(V:\) volume) then:
| 1. | \(∆U_1 > ∆U_2\) | 2. | \(∆U_1 < ∆U_2\) |
| 3. | \(∆U_1 = ∆U_2\) | 4. | \(∆U_1 \leq ∆U_2\) |
| 1. | \(12~\text{J}\) | 2. | \(24~\text{J}\) |
| 3. | \(36~\text{J}\) | 4. | \(0~\text{J}\) |
(where symbols have their usual meanings)
1. \(C_P = \frac{\gamma R}{\gamma-1 }\)
2. \(C_P-C_V= R\)
3. \(\Delta U = \frac{P_fV_f-P_iV_i}{1-\gamma}\)
4. \(C_V = \frac{R}{\gamma-1 }\)
If 3 moles of a monoatomic gas do 150 J of work when it expands isobarically, then a change in its internal energy will be:
| 1. | 100 J | 2. | 225 J |
| 3. | 400 J | 4. | 450 J |
If \(n\) moles of an ideal gas is heated at a constant pressure from \(50^\circ\text C\) to \(100^\circ\text C,\) the increase in the internal energy of the gas will be:
\(\left(\frac{C_{p}}{C_{v}} = \gamma\ ~\text{and}~\ R = \text{gas constant}\right)\)
| 1. | \(\dfrac{50nR}{\gamma - 1}\) | 2. | \(\dfrac{100nR}{\gamma - 1}\) |
| 3. | \(\dfrac{50n\gamma R}{\gamma - 1}\) | 4. | \(\dfrac{25n\gamma R}{\gamma - 1}\) |
In the \(P\text-V\) graph shown for an ideal diatomic gas, the change in the internal energy is:
| 1. | \(\frac{3}{2}P(V_2-V_1)\) | 2. | \(\frac{5}{2}P(V_2-V_1)\) |
| 3. | \(\frac{3}{2}P(V_1-V_2)\) | 4. | \(\frac{7}{2}P(V_1-V_2)\) |
If the ratio of specific heat of a gas at constant pressure to that at constant volume is , the change in internal energy of a mass of gas, when the volume changes from V to 2V at constant pressure, P is:
| 1. | 2. | PV | |
| 3. | 4. |
When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is:
| 1. | \(\dfrac{2}{5}\) | 2. | \(\dfrac{3}{5}\) |
| 3. | \(\dfrac{3}{7}\) | 4. | \(\dfrac{5}{7}\) |
The pressure in a monoatomic gas increases linearly from 4 atm to 8 atm when its volume increases from 0.2 m to 0.5 m. The increase in internal energy will be:
| 1. | 480 kJ | 2. | 550 kJ |
| 3. | 200 kJ | 4. | 100 kJ |
If 32 gm of \(O_2\) at \(27^{\circ}\mathrm{C}\) is mixed with 64 gm of \(O_2\) at \(327^{\circ}\mathrm{C}\) in an adiabatic vessel, then the final temperature of the mixture will be:
1. \(200^{\circ}\mathrm{C}\)
2. \(227^{\circ}\mathrm{C}\)
3. \(314.5^{\circ}\mathrm{C}\)
4. \(235.5^{\circ}\mathrm{C}\)
© 2025 GoodEd Technologies Pvt. Ltd.