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For an adiabatic process, the work done by an ideal gas is given by the change in internal energy with a negative sign, or specifically using the temperature change: $$W = \frac{nR(T_1 - T_2)}{\gamma - 1}$$
Given: $n = 1$ mole $T_1 = 60$ K $T_2 = 50$ K $\gamma = 5/3$ $R = 8.3$ J mol⁻¹ K⁻¹
The value of $(\gamma - 1)$ is: $$\gamma - 1 = \frac{5}{3} - 1 = \frac{2}{3}$$
Substitute the values into the equation: $$W = \frac{1 \times 8.3 \times (60 - 50)}{2/3}$$ $$W = \frac{8.3 \times 10}{2/3}$$ $$W = \frac{83 \times 3}{2}$$ $$W = \frac{249}{2} = 124.5 \text{ J}$$
Final Answer: 124.5 J