Question

In an adiabatic process, 4g of H, gas expands and temperature changes from 47°C to 27°C. Find the magnitude of
the work done by the gas on the surroundings.​

Answer 1

Given info : In a adiabatic process, 4g of H₂ gas expands and temperature changes from 47°C to 27°C.

To find : the magnitude of the work donw by the gas on the surroundings is..

solution : no of moles of H₂ gas = mass of H₂ gas/molar mass of H₂

= 4g/2g/mol = 2 mol

molar heat capacity of of H₂ gas at constant volume, $C_v$= 5R/2 [∵ H₂ is diatomic gas ]

we know, adiabatic process, Q = 0

∴ ΔU = W [ from 1st law of thermodyanmics ]

we know, change in internal energy , ΔU = $nC_v\Delta T$

= 2 × 5R/2 × (47°C - 27°C)  Joules [ change in temperature for celcius and kelvin are same. so we can choose either of them in this case ]

= 100R Joules

= 100 × 8.314 Joules

= 831.4 Joules.

therefore the workdone by the gas on the surroundings is 831.4 Joules.