At a constant pressure, what should be the percentage increase in the temperature in kelvin for a 10% increase in volume?

$$\begin{gathered} \mathrm{At} \mathrm{a} \mathrm{constant} \mathrm{pressure}; \\ \mathrm{Initial} \mathrm{volume}={\mathrm{V}}_1 \\ \mathrm{Final} \mathrm{volume}= {\mathrm{V}}_2={\mathrm{V}}_1+10\%{\mathrm{V}}_1={\mathrm{V}}_1+\left(\frac{10}{100}{\mathrm{V}}_1\right) \\ \mathrm{As} \mathrm{we} \mathrm{know}, \\ \frac{{\mathrm{V}}_1}{{\mathrm{V}}_2}=\frac{{\mathrm{T}}_1}{{\mathrm{T}}_2} \\ \Rightarrow \frac{{\mathrm{V}}_1}{{\mathrm{V}}_1+0.1{\mathrm{V}}_1}=\frac{{\mathrm{T}}_1}{{\mathrm{T}}_2} \end{gathered}$$U

$$\begin{gathered} \frac{10}{11}=\frac{{\mathrm{T}}_1}{{\mathrm{T}}_2} \\ \Rightarrow \frac{11}{10}-1=\frac{{\mathrm{T}}_2}{{\mathrm{T}}_1}-1 \\ \frac{1}{10}=\frac{{\mathrm{T}}_2-{\mathrm{T}}_1}{{\mathrm{T}}_1} \\ \mathrm{on} \mathrm{taking} \mathrm{percentage} \\ 10=\left(\frac{∆\mathrm{T}}{{\mathrm{T}}_{\mathrm{initial}}}\right)\% \end{gathered}$$

10% temperature increase is required to increase volume by 10%.