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प्रश्न
What will be the work done on an ideal gas enclosed in a cylinder, when it is compressed by a constant external pressure, pext in a single step as shown in figure. Explain graphically.
उत्तर
Assumption: Cylinder is filled with one mole gas, and the piston is frictionless. Let the pressure of gas inside be p and the volume of gas be \[\ce{V_{I}}\].
Piston is moved towards the inside to make the external pressure \[\ce{(P_{ext})}\] equal to p. Now, let us assume that this change takes place in a single step, hence, \[\ce{V}\] is the final volume. The work done by the piston is depicted in the graph shown below by shading the area.
PextΔV = AV1 × (V1 – V2)
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संबंधित प्रश्न
For an ideal gas, the work of reversible expansion under isothermal condition can be calculated by using the expression w = `- nRT` In `V_f/V_i`. A sample containing 1.0 mol of an ideal gas is expanded isothermally and reversibly to ten times of its original volume, in two separate experiments. The expansion is carried out at 300 K and at 600 K respectively.
(i) Work done at 600 K is 20 times the work done at 300 K.
(ii) Work done at 300 K is twice the work done at 600 K.
(iii) Work done at 600 K is twice the work done at 300 K.
(iv) ∆U = 0 in both cases.
Expansion of a gas in vacuum is called free expansion. Calculate the work done and the change in internal energy when 1 litre of ideal gas expands isothermally into vacuum until its total volume is 5 litre?
How will you calculate work done on an ideal gas in a compression, when change in pressure is carried out in infinite steps?
1.0 mol of a monoatomic ideal gas is expanded from state (1) to state (2) as shown in figure. Calculate the work done for the expansion of gas from state (1) to state (2) at 298 K.
An ideal gas is allowed to expand against a constant pressure of 2 bar from 10 L to 50 L in one step. Calculate the amount of work done by the gas. If the same expansion were carried out reversibly, will the work done be higher or lower than the earlier case? (Given that 1 L bar = 100 J)
Match the following :
| A | B |
| (i) Adiabatic process | (a) Heat |
| (ii) Isolated system | (b) At constant volume |
| (iii) Isothermal change | (c) First law of thermodynamics |
| (iv) Path function | (d) No exchange of energy and matter |
| (v) State function | (e) No transfer of heat |
| (vi) ΔU = q | (f) Constant temperature |
| (vii) Law of conservation of energy | (g) Internal energy |
| (viii) Reversible process | (h) Pext = o |
| (ix) Free expansion | (i) At constant pressure |
| (x) ΔH = q | (j) Infinitely slow process which proceeds through a series of equilibrium states. |
| (xi) Intensive property | (k) Entropy |
| (xii) Extensive property | (l) Pressure |
| (m) Specific heat |
For silver Cp (J K-1 mol-1) = 23 + 0.01 T. If the temperature (T) of 3 moles of silver is raised from 300 K to 1000 K at 1 atom pressure, the value of ΔH will be close to ______.
Calculate the work involved when 1 mol of an ideal gas is compressed reversibly from 1.00 bar to 5.00 bar at a constant temperature of 300 K ______.
1 mole of an ideal monoatomic gas initially at 1 atm and 300 K experiences a process by which pressure is doubled. The nature of the process is unspecified but 6. ΔU = 900 cal. The final volume will be ______ l.
[Given : R = 0.08 atm lit. I mol/K = 2 Cal/K/mol J]
Find the work done when 2 moles of hydrogen expand isothermally from 15 to 50 litres against a constant pressure of 1 atm at 25°C.
