Question

8.
Temperature of n moles of an ideal gas is increased
(a is
from To to 2T, through a process P =
+ve constant). Find the work done by gas.
(1) 3nRT.
(2) 3nRTIN (2)
(3) -3nRT,
(4) -3nRT ln(2)​

Answer 1

Answer:

The work done by gas is 3 n R T

Explanation:

Given as :

Temperature of n moles of an ideal gas increases from T to 2 T

from ideal gas equation

P V = n R ΔT                     ,, where P = pressure     , n = number of moles

                                                    V = volume        , R = constant

                                                    ΔT = change in temperature

Change in temperature=  $T_2 - T_1$

or,                                 ΔT  = 2 T - T = T

For given process , PT = a = constant

idea equation

P² V = constant

or,

P $V^{\frac{1}{2}}$ = constant

Now, Molar heat capacity = C = $\dfrac{R}{1-x}$ + $C_v$

i.e C = $\dfrac{R}{1-\dfrac{1}{2} }$ + $C_v$

Or, C = 2 R + $C_v$

heat absorbed = ΔQ = n C ΔT

Or, ΔQ = n $C_v$ ΔT + ΔW

Or, ΔW = n C ΔT - n $C_v$ ΔT

or,  ΔW =  3 n R T

Hence, The work done by gas is 3nRT  Answer