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प्रश्न
How will you calculate work done on an ideal gas in a compression, when change in pressure is carried out in infinite steps?
उत्तर
When a process can be reversed by bringing an extremely small change in it, we call it a reversible process. The pressure-volume graph can be used to calculate the work done. The pressure is not constant, and changes in infinitesimal amounts as compression happens from initial volume Vi to the final volume Vf. The below graph depicts the work done with the shaded area.
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संबंधित प्रश्न
The pressure-volume work for an ideal gas can be calculated by using the expression w = `- int_(v_i)^(v_f) p_(ex) dV`. The work can also be calculated from the pV– plot by using the area under the curve within the specified limits. When an ideal gas is compressed (a) reversibly or (b) irreversibly from volume Vi to Vf. choose the correct option.
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.
A sample of 1.0 mol of a monoatomic ideal gas is taken through a cyclic process of expansion and compression as shown in figure 6.1. What will be the value of ∆H for the cycle as a whole?
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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)
Graphically show the total work done in an expansion when the state of an ideal gas is changed reversibly and isothermally from \[\ce{(p_i, V_i)}\] to \[\ce{(p_f , V_f )}\]. With the help of a pV plot compare the work done in the above case with that carried out against a constant external pressure \[\ce{p_f}\].
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]
An ideal gas expands in volume from 1 × 10−3 to 1 × 10−2 m3 at 300 K against a constant pressure of 1 × 105 Nm−2. The work done is ______.
