A spherical shell of copper is completely filled with a liquid at a temperature t°C. The bulk modulus of the liquid is K and coefficient of volume expansion is $\gamma$ . If the temperature of the liquid and the shells increased by $∆\mathrm{T}$, then the outward pressure $∆\mathrm{p}$ on the shell that results from the temperature increase is given by ($\alpha$ is the coefficient of linear expansion of the material for the shell):