I'm working out how much time a pendulum clock will gain or loose due to change of the length of the pendulum due to temperature. so far I've got, new time period, $$T_2=T_1(1+\frac12\alpha\Delta T)$$
due to $\Delta T$ change in temperature, when the coefficient of linear expansion of the pendulum material is $\alpha$. $T_1$ is the time period when there is no change in temperature.
Now, I can not understand how the time period of the pendulum and the time measured by the clock is related. Please help me with this and also mention if I am going correct or not.