Question

10 moles of an ideal gas expand adiabatically from an initial temperature 100k to a final temperature 200k. If cv is the molar specific heat capacity of the gas at constant volume the work done by the gas is

Answer 1

Answer:1000Cv

Explanation:

From first law of thermodynamics,

ΔU=q+W

As we know that, for adiabatic condition,

q=0

∴ΔU=W.....(1)

At constant volume,

ΔU=nCvΔT.....(2)

From eqn (1)&(2), we have

W=nCvΔT.....(3)

W=10*Cv*100

∴ W=1000Cv.

Answer 2

Given :

Number of moles (n) = 10 moles

Initial temperature (T₁) = 100 K

Final Temperature (T₂) = 200 K

To Find :

Work done by the gas

Solution :

According to first law of thermodynamics,

Change in internal Energy (ΔU) = Heat (Q) + Work done (W)

We know, In an Adiabatic process,  Q = 0

∴    ΔU   =   W   ---------- (i)

At constant volume,

ΔU   =  n$C_v$ΔT    ---------- (ii)      

Where, n = number of moles; $C_v$ = Molar specific heat capacity; ΔT = Change in temperature

From equation (i) & (ii), we have

Work done (W) = n$C_v$ΔT  

                         = 10 × $C_v$ × (200 - 100)

                         =  1000$C_v$

Therefore, the work done by the gas is 1000$C_v$ J.