Given information:
The relation between volume (v) and temperature (t) is given by v = kt^(2/3), where k is a constant.

To calculate the work done when the temperature changes by 60 I, we need to find the change in volume and then calculate the work done.

Let's assume the initial temperature is t1 and the final temperature is t2. The change in temperature is given by Δt = t2 - t1 = 60 I.

To find the change in volume, we substitute the initial temperature (t1) and the final temperature (t2) in the given relation.

Initial volume: v1 = k(t1)^(2/3)
Final volume: v2 = k(t2)^(2/3)

The change in volume is given by Δv = v2 - v1 = k(t2)^(2/3) - k(t1)^(2/3)

Now, let's simplify the expression for Δv:
Δv = k(t2)^(2/3) - k(t1)^(2/3)
= k[(t2)^(2/3) - (t1)^(2/3)]

Calculating the work done:
Work done (W) is given by the formula: W = PΔv, where P is the pressure.

However, since the pressure is not given in the question, we cannot calculate the exact value of work done. We can only determine the ratio of work done.

Let's assume the work done is W1 when the temperature changes by 1 I. Then the work done when the temperature changes by 60 I can be calculated as follows:

W = (60I / 1I) * W1
= 60 * W1

Therefore, the work done when the temperature changes by 60 I is 60 times the work done when the temperature changes by 1 I.

Answer: The work done when the temperature changes by 60 I is 60 times the work done when the temperature changes by 1 I.