Question

How much water will spill from a 5.00 L vat if the temperature increased by 35.0°C?

Answer 1

The initial volume of the vat is $V_0.$ By increasing the temperature, the volume of the vat increases, decreasing the inner space:

$$V=V_0(1+\alpha \Delta t)^3,\\ \Delta V=V-V_0=V_0\alpha^3 t^3,\\ \Delta V=5\alpha^3·35^3=214375\alpha ^3.$$

For a copper vat, the volume of the spilled water will be 9.98·10^-10 L.