Heat and Thermodynamics

We know that in adiabatic expansion, there is no heat exchange. So, ∆Q=0.
From the first law of thermodynamics:
∆Q=∆U+W Since ∆Q=0, this means: 0=∆U+W So, W=−∆U
The change in internal energy for n moles of a diatomic gas is: ∆U=nCV∆T where CV for a diatomic gas is ‌

5

2

R.
Here, n=3 moles and the temperature change ∆T=−50∘C (or -50 in Kelvin, since the size of the degree is the same).
So, W=−∆U=−nCV∆T=−3×‌

5

2

R×(−50)
Multiplying out: −3×‌

5

2

R×(−50)=7.5R×50=375R
The work done by the gas is 375R.