Question

Calculate the work done when 1 liter of monoatomic perfect gas at NTP is compressed adiabatically

to ½ of its volume. (use γ = 1.67)​

Answer 1

Given:

Volume of the monoatomic gas at NTP = 1 liter

To find:

Work done when the gas is compressed adiabatically to half of its volume.

Solution:

As we know that work done is an adiabatic process is:

W =[ nRΔT / ( γ- 1) ]

Since the gas is monoatomic, n=1:

= [1*8.3*ΔT / 1.67- 1]

We know that for an adiabatic process:

T V^(γ-1) = c

∴(293* V^(1.67-1)) = (T final * (V/2)^1.67-1)

T final = 293(V^0.67 / (V/2)^0.67 )

T final = 293* 2^0.67

T final = 466.2 K

ΔT = T final - T initial

ΔT = 466.2 - 293 = 173.2 K

Work = 1* 8.3 * 173.2 / 1.67 - 1

Work = 2246.19 J

Therefore the work done on the gas is 2246.19 J.