Q. No.A diatomic gas with rigid molecules undergoes expansion at constant pressure, performing \(10~\text{J}\) of work in the process. What is the amount of heat energy absorbed by the gas during this process?
1. \(35~\text{J}\)
2. \(40~\text{J}\)
3. \(25~\text{J}\)
4. \(30~\text{J}\)
1. \(35~\text{J}\)
2. \(40~\text{J}\)
3. \(25~\text{J}\)
4. \(30~\text{J}\)
A sample of an ideal gas is taken through the cyclic process \(abca\) as shown in the figure. The change in the internal energy of the gas along the path \(ca\) is \(-180~\text{J}\). The gas absorbs \(250~\text{J}\) of heat along the path \(ab\) and \(60~\text{J}\) along the path \(bc\). The work done by the gas along the path \(abc\) is:
1. \(140~\text{J}\)
2. \(130~\text{J}\)
3. \(100~\text{J}\)
4. \(120~\text{J}\)
Two moles of helium gas are mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of the mixture at constant volume? (\(R = 8.3~\text{J/mol K}\))
1. \(21.6~\text{J/mol K}\)
2. \(19.7~\text{J/mol K}\)
3. \(15.7~\text{J/mol K}\)
4. \(17.4~\text{J/mol K}\)
An engine takes in \(5\) moles of air at \(20^\circ\) C and \(1\) atm, and compresses it adiabaticaly to \(1/10\) th of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be:
1. \(46~ \text{J}\)
2. \(46~\text{kJ}\)
3. \(23~\text{J}\)
4. \(23~\text{kJ}\)
A balloon filled with helium (\(32^\circ \mathrm{C}\) and \(1.7\) atm) bursts. Immediately afterwards the expansion of helium can be considered as:
| 1. | irreversible adiabatic |
| 2. | reversible adiabatic |
| 3. | irreversible isothermal |
| 4. | reversible isothermal |
If minimum possible work is done by a refrigerator in converting \(100\) grams of water at \(0^\circ \mathrm{C}\) to ice, how much heat (in calories) is released to the surroundings at temperature \(27^\circ \mathrm{C}\) (Latent heat of ice = \(80\) cal/gram) to the nearest integer?
1. \(3242\)
2. \(8791\)
3. \(1634\)
4. \(100\)
Three different processes that can occur in an ideal monoatomic gas are shown in the \(P\) vs \(V\) diagram. The paths are labelled as \(A \rightarrow B, A \rightarrow C\) and \(A\rightarrow D\). The change in internal energies during these process are taken as \(E_{AB}\), \(E_{AC}\) and \(E_{AD}\) and the work done as \(W_{A B}, W_{A C}\) and \( W_{A D}\). The correct relation between these parameters are:
| 1. | \(E_{A B}=E_{A C}=E_{A D}, W_{A B}>0, W_{A C}=0, W_{A D}<0\) |
| 2. | \(E_{A B}<E_{A C}<E_{A D}, W_{A B}>0, W_{A C}>W_{A D}\) |
| 3. | \(E_{A B}=E_{A C}<E_{A D},W_{A B}>0,W_{A C}=0, W_{A D}<0\) |
| 4. | \(E_{A B}>E_{A C}>E_{A D}, \quad W_{A B}< W_{A C}< W_{A D}\) |
In an adiabatic process, the density of a diatomic gas becomes \(32\) times its initial value. The final pressure of the gas is found to be \(n\) times the initial pressure. The value of \(n\) is:
1. \(326\)
2. \(\dfrac{1}{32}\)
3. \(32\)
4. \(128\)
A closed vessel contains \(0.1\) mole of a monatomic ideal gas at \(200\) K. If \(0.05\) mole of the same gas at \(400\) K is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be closed to:
1. \(133\)
2. \(57\)
3. \(266\)
4. \(504\)
\(n\) moles of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes.
| \(A\rightarrow B\) | Isothermal expansion at temperature \(T\) so that the volume is doubled from \(V_1\) to \(V_2=2V_1\) and pressure changes from \(P_1\) to \(P_2.\) |
| \(B\rightarrow C\) | Isobaric compression at pressure \(P_2\) to initial volume \(V_1\). |
| \(C\rightarrow A\) | Isochoric change leading to change of pressure from \(P_2\) to \(P_1\). |
Total work done in the complete cycle \(ABCA\) is:
1. \(0\)
2. \(nRT(\ln 2-\frac{1}{2})\)
3. \(nRT\ln 2\)
4. \(nRT(\ln 2+\frac{1}{2})\)
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