1. **Problem statement:** A gas sample initially has volume $V_1=0.26$ m³, pressure $P=140000$ Pa, and temperature $T_1=24^\circ C$. It is heated at constant pressure to $T_2=75^\circ C$. The gas mass is $m=0.45$ kg and gas constant $R=287$ J/kg·K. We need to find: i. Initial specific volume $v_1$. ii. Final volume $V_2$ after heating. iii. Work done by the gas during heating. 2. **Convert temperatures to Kelvin:** $$T_1=24+273.15=297.15\,K$$ $$T_2=75+273.15=348.15\,K$$ 3. **Calculate initial specific volume $v_1$:** Specific volume is volume per unit mass: $$v_1=\frac{V_1}{m}=\frac{0.26}{0.45}=0.5778\,m^3/kg$$ 4. **Calculate final volume $V_2$ using Charles's Law:** At constant pressure and mass, volume is proportional to temperature: $$\frac{V_1}{T_1}=\frac{V_2}{T_2} \implies V_2=V_1 \times \frac{T_2}{T_1}$$ Substitute values: $$V_2=0.26 \times \frac{348.15}{297.15}=0.26 \times 1.1719=0.3047\,m^3$$ 5. **Calculate work done by the gas during heating:** Work done at constant pressure is: $$W=P\Delta V=P(V_2 - V_1)$$ Substitute values: $$W=140000 \times (0.3047 - 0.26)=140000 \times 0.0447=6258\,J$$ **Final answers:** - Initial specific volume $v_1=0.5778$ m³/kg - Final volume $V_2=0.3047$ m³ - Work done $W=6258$ J