Q.A sample of gas has a volume of 8.5 dm$^3$ at an unknown temperature. When the sample is submerged in ice water at 0 $^\circ$C, its volume gets reduced to 6.37 dm$^3$. What is its initial temperature?

Step 1. At constant pressure, Charles's law gives $\dfrac{V_1}{T_1}=\dfrac{V_2}{T_2}$, so $T_1=\dfrac{V_1T_2}{V_2}$.

Step 2. Here $V_1=8.5\ \text{dm}^3$ (unknown initial temperature $T_1$), and $V_2=6.37\ \text{dm}^3$ at $T_2=0\,^\circ\text{C}=273$ K.

Step 3. $T_1=\dfrac{8.5\times273}{6.37}=\dfrac{2320.5}{6.37}\approx364.3$ K. …

Apply Charles's law with the known final state (ice water, 273 K) to solve fo …

• Mixing up which volume/temperature pair is state 1 and which is state 2, which inverts the ratio and gives a temperature below 273 K instead of above it …