Introduction:
In this problem, we are given a second pendulum operated at 30 degrees Celsius, and we need to find the gain or loss in 1 day. The alpha value of steel is given as 1.2×10^5 c. To solve this problem, we will use the formula for the thermal expansion of a pendulum.

Thermal Expansion of a Pendulum:
The length of a pendulum changes with temperature due to thermal expansion. The change in length (∆L) of a pendulum is given by the formula:

∆L = α * L * ∆T

Where:
∆L = Change in length of the pendulum
α = Coefficient of linear expansion of the material
L = Initial length of the pendulum
∆T = Change in temperature

Calculation:
Given:
Initial temperature = 20 degrees Celsius
Final temperature = 30 degrees Celsius
Coefficient of linear expansion (α) = 1.2×10^5 c (per degree Celsius)

Step 1: Calculate the change in temperature (∆T):
∆T = Final temperature - Initial temperature
∆T = 30°C - 20°C
∆T = 10°C

Step 2: Calculate the change in length (∆L):
∆L = α * L * ∆T

Step 3: Calculate the gain or loss in 1 day:
To find the gain or loss in 1 day, we need to multiply the change in length (∆L) by the number of seconds in a day and divide by the initial length (L).

Number of seconds in a day = 24 hours * 60 minutes * 60 seconds = 86400 seconds

Gain or loss in 1 day = (∆L * 86400) / L

Step 4: Substitute the values to calculate the gain or loss in 1 day:
Gain or loss in 1 day = (∆L * 86400) / L

Conclusion:
By following the above steps, we can determine the gain or loss in 1 day for a second pendulum operated at 30 degrees Celsius. The gain or loss will be given by the formula (∆L * 86400) / L, where ∆L is the change in length calculated using the formula ∆L = α * L * ∆T, and α is the coefficient of linear expansion of the material.

6×10^5×24 hours