An ideal gas undergoes four different processes from the same initial state (figure). Four processes are adiabatic, isothermal, isobaric and isochoric. Out of \(1,\) \(2,\) \(3\) and \(4,\) which one is adiabatic?
1. | \(4\) | 2. | \(3\) |
3. | \(2\) | 4. | \(1\) |
If an average person jogs, he produces \(14.5 \times10^3\) cal/min. This is removed by the evaporation of sweat. The amount of sweat evaporated per minute (assuming \(1\) kg requires \(580 \times10^3\) cal for evaporation) is:
1. | \(0.25\) kg | 2. | \(0.50\) kg |
3. | \(0.025\) kg | 4. | \(0.20\) kg |
Consider the \((P\text-V)\) diagram for an ideal gas shown in the figure.
1. | 2. | ||
3. | 4. |
1. \(T = \dfrac{T_{1} + T_{2} + T_{3}}{3}\)
2. \(T = \dfrac{M_{1} T_{1} + M_{2} T_{2} + M_{3} T_{3}}{M_{1} + M_{2} + M_{3}}\)
3. \(T = \dfrac{M_{1} T_{1} + M_{2} T_{2} + M_{3} T_{3}}{3 \left(\right. M_{1} + M_{2} + M_{3} \left.\right)}\)
4. \(T = \dfrac{M_{1} T_{1} s + M_{2} T_{2} s + M_{3} T_{3} s}{M_{1} + M_{2} + M_{3}}\)
(a) | The increase in temperature of an iron rod by hammering it. |
(b) | A gas in a small container at a temperature \(T_1\) is brought in contact with a big reservoir at a higher temperature \(T_2\) which increases the temperature of the gas. |
(c) | A quasi-static isothermal expansion of an ideal gas in a cylinder fitted with a frictionless piston. |
(d) | An ideal gas is enclosed in a piston-cylinder arrangement with adiabatic walls. A weight \(w\) is added to the piston, resulting in the compression of gas. |
1. | (a), (b), (c) | 2. | (a), (d) |
3. | (b), (c), (d) | 4. | (a), (b), (d) |
(a) | \(dU = 0 \) | (b) | \(dQ = 0\) |
(c) | \(dQ = dU \) | (d) | \(dQ = dW\) |
1. | (a), (b), (c) | 2. | (a), (d) |
3. | (b), (c), (d) | 4. | (a), (c), (d) |
The figure shows the \((P\text-V)\) diagram of an ideal gas undergoing a change of state from \(A\) to \(B\). Four different paths \(\mathrm{I, II, III}\) and \(\mathrm{IV}\), as shown in the figure, may lead to the same change of state.
(a) | The change in internal energy is the same in cases \(\mathrm{IV}\) and \(\mathrm{III}\) but not in cases \(\mathrm{I}\) and \(\mathrm{II}\). |
(b) | The change in internal energy is the same in all four cases. |
(c) | Work done is maximum in case \(\mathrm{I}\). |
(d) | Work done is minimum in case \(\mathrm{II}\). |
Which of the following options contains only correct statements?
1. (b), (c), (d)
2. (a), (d)
3. (b), (c)
4. (a), (c), (d)
Consider a cycle followed by an engine (figure).
1 to 2 is isothermal,
2 to 3 is adiabatic,
3 to 1 is adiabatic.
Such a process does not exist, because:
(a) | heat is completely converted to mechanical energy in such a process, which is not possible. |
(b) | In this process, mechanical energy is completely converted to heat, which is not possible. |
(c) | curves representing two adiabatic processes don’t intersect. |
(d) | curves representing an adiabatic process and an isothermal process don't intersect. |
Choose the correct alternatives:
1. | (a), (b) | 2. | (a), (c) |
3. | (b), (c) | 4. | (c), (d) |