Advertisements
Advertisements
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.
उत्तर
(iii) Work done at 600 K is twice the work done at 300 K.
(iv) ∆U = 0 in both cases.
Explanation:
For isothermal reversible change, we know
q = – w = `nRT` In `V_f/V_i` = 2.303 `nRT` log `V_f/V_i`
`(W_(600 K))/(W_(300 K)) = (1 xx R xx 600 K In 1/10)/(1 xx R xx 300 K In 1/10) = 600/300` = 2
For isothermal expansion of ideal gases, ΔU = 0.
Since temperature is constant this means there is no change in internal energy.
APPEARS IN
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.
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?
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?
Represent the potential energy/enthalpy change in the following processes graphically.
(a) Throwing a stone from the ground to roof.
(b) \[\ce{1/2 H2(g) + 1/2 Cl2 (g) ⇌ HCl (g) Δ_rH^Θ = - 92.32 kJ mol^{-1}}\]
In which of the processes potential energy/enthalpy change is contributing factor to the spontaneity?
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 |
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.
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 ______.
